WAEC SSCE - Physics - 2006
Pregunta 1 Informe
An atom \(^{234}_{91} P\) emits a gamma radiation. The resultant nuclide is
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Pregunta 2 Informe
A solid body will float in a liquid if its
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A solid body will float in a liquid if its density is less than that of the liquid. Density is the measure of how much mass is packed into a certain volume. When a solid object is placed in a liquid, it will either float or sink depending on the relative densities of the object and the liquid. If the object has a higher density than the liquid, it will sink because it has more mass packed into the same volume as the liquid. However, if the object has a lower density than the liquid, it will float because it has less mass packed into the same volume as the liquid. Therefore, for a solid body to float in a liquid, its density must be less than that of the liquid.
Pregunta 3 Informe
An electric lamp rated 120W is used on a 240Vrms, calculate the resistance of its filament
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Pregunta 4 Informe
A block of volume 3 x 105m3 and density 2.5 x 103 kg m-3 is suspended from a spring balance with \(\frac{2}{3}\) of its volume immersed in a liquid of density 900 kg m-3. Determine the reading of the spring balance [g = 10ms-2]
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Pregunta 5 Informe
The amount of energy required to change a kilogram of ice in water without a change in temperature is
Detalles de la respuesta
The amount of energy required to change a kilogram of ice into water without a change in temperature is the specific latent heat of fusion of ice. When a substance changes from one phase to another, it requires energy to break the bonds between the molecules in the original phase and form new bonds in the new phase. In the case of ice changing into water, the bonds between the molecules in the solid ice must be broken in order to form liquid water. The specific latent heat of fusion of ice is the amount of energy required to change a kilogram of ice into water without a change in temperature. This value is specific to the substance and phase transition, and represents the amount of energy required to break the bonds between the molecules in the solid phase and form a liquid. Therefore, to change a kilogram of ice into water without a change in temperature, you would need to add energy equal to the specific latent heat of fusion of ice. Option (D) specific latent heat of fusion of ice is the correct answer.
Pregunta 6 Informe
Which of the following source of energy is renewable?
Detalles de la respuesta
The source of energy that is renewable is hydro power. Hydro power is generated by the movement of water, usually by falling water turning turbines to generate electricity. This movement of water can come from rivers, waterfalls, tides or even man-made dams. The water cycle replenishes the water used to generate hydro power, making it a renewable energy source. In contrast, petroleum and charcoal are non-renewable energy sources that are derived from fossil fuels. These fuels are finite and take millions of years to form. Once we use up all the available fossil fuels, they will not be replenished within our lifetimes. Nuclear energy, while not derived from fossil fuels, also involves the use of finite resources like uranium, making it a non-renewable source of energy. Therefore, hydro power is the renewable source of energy, while the others are non-renewable.
Pregunta 7 Informe
Which of the following actions is necessary in order to tune a string to produce a note of an octave higher than its fundamental?
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Pregunta 8 Informe
Which of the following physical quantities are derived? i. Area ii. Thrust iii. Pressure iv. Mass
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Area, thrust, pressure, and mass are physical quantities. Area is a derived physical quantity as it is calculated as the product of two lengths, such as width and height. The unit of area is typically square meters (m²), which is derived from the base unit of length (m). Thrust is also a derived physical quantity, as it is a force that is generated by the propulsion system of a vehicle or engine. It is typically measured in newtons (N), which is derived from the base units of mass (kg) and acceleration (m/s²). Pressure is a derived physical quantity as it is calculated as the force per unit area. Pressure is typically measured in pascals (Pa), which is derived from the base units of force (N) and area (m²). Mass, on the other hand, is a fundamental physical quantity that cannot be derived from any other physical quantity. It is a measure of the amount of matter in an object and is typically measured in kilograms (kg).
Pregunta 9 Informe
Fusion is not usually used for generating electric power because
Detalles de la respuesta
Fusion is the process of combining atomic nuclei to form a heavier nucleus, which releases a large amount of energy in the form of radiation. Although fusion is a powerful source of energy, it is not currently used for generating electric power on a large scale. One reason for this is that very high temperatures, typically in excess of 100 million degrees Celsius, are required to initiate and maintain a fusion reaction. These extreme temperatures are difficult to achieve and maintain for prolonged periods of time, and they require a significant amount of energy to create and sustain. This makes fusion an expensive and technically challenging source of power. In addition, the raw materials required for fusion, such as hydrogen isotopes, are not easily available in large quantities. Furthermore, the process of extracting and processing these materials can also be expensive and energy-intensive. Finally, heavy nuclei, such as those of uranium and plutonium, are not involved in fusion reactions. Instead, fusion typically involves the lighter elements such as hydrogen isotopes. Heavy nuclei are used in fission reactions, which is another process for generating nuclear power. In summary, while fusion is a powerful source of energy, the technical challenges and high costs associated with generating and maintaining the extreme temperatures required for fusion make it an impractical source of power at present.
Pregunta 10 Informe
Which of the following observations cannot be explained using the rectilinear propagation of light?
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Pregunta 11 Informe
An object is said to undergo oscillatory motion when it moves
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An object undergoes oscillatory motion when it moves to and fro about a fixed point. The motion of the object repeats itself periodically, meaning that it moves back and forth over the same path multiple times. The fixed point is called the equilibrium position, and the maximum distance from the equilibrium position that the object moves is called the amplitude of the oscillation. For example, a pendulum oscillates back and forth about its equilibrium position, which is the vertical hanging position. As it swings, it moves back and forth along the same path, and the distance it moves from the equilibrium position is its amplitude. Oscillatory motion is a common phenomenon in many natural and man-made systems, such as springs, musical instruments, and electric circuits. Understanding oscillatory motion is important in many fields, including physics, engineering, and biology.
Pregunta 12 Informe
The breaking up of an atomic nucleus into the fragment of nearly equal size is known as
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The breaking up of an atomic nucleus into the fragments of nearly equal size is known as nuclear fission. This process involves the splitting of a heavy nucleus, such as uranium or plutonium, into two lighter nuclei, called fission products, as well as the release of a large amount of energy in the form of heat and radiation. Nuclear fission can be induced by bombarding a nucleus with a neutron, which causes the nucleus to become unstable and split apart. The neutrons released from the fission can then go on to cause additional fissions in a chain reaction, releasing even more energy. Nuclear fission is the process that powers nuclear reactors and nuclear weapons. It is also responsible for the release of energy in certain natural phenomena, such as the decay of radioactive isotopes in the earth's crust and the energy output of stars.
Pregunta 13 Informe
An electron of mass m and charge \(\Box\) enters a uniform electric field between two metal plates P and q separated by a distance d. P is maintained at a potential V while Q is earthed. Determine an expression for the magnitude of the acceleration of electron through the field
Detalles de la respuesta
The electric field between the two metal plates exerts a force on the electron which accelerates it. According to Newton's second law, the magnitude of the acceleration (a) of an object is proportional to the net force (F) acting on it, and inversely proportional to its mass (m), i.e., a = F/m. In this case, the net force acting on the electron is the electric force (Fe) given by Fe = qE, where q is the charge of the electron and E is the magnitude of the electric field between the plates. Since the electron has a negative charge, the direction of the force is opposite to the direction of the field, so the electron is accelerated towards the negative plate. The electric field between the plates is given by E = V/d, where V is the potential difference between the plates and d is the distance between them. Therefore, the force on the electron is given by Fe = q(V/d). Substituting this expression for Fe into the equation for acceleration, we get: a = Fe/m = q(V/d) / m Since the charge of an electron is -e (where e is the elementary charge), we can substitute -e for q to get: a = (-e)(V/d) / m Simplifying this expression, we get: a = - (eV/md) So the magnitude of the acceleration of the electron is given by: a = (eV/md) Therefore, the correct option is (a) \(\frac{eV}{md}\).
Pregunta 14 Informe
A body is rotating in a horizontal circle of radius 2.5m with an angular speed of 5 rad s-1. Calculate the magnitude of the radial acceleration of the body
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Pregunta 15 Informe
Which of the following statements about a bar magnet is correct?
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The correct statement about a bar magnet is "the magnetic properties are more pronounced at points near the end of the bar". A bar magnet has two poles: a north pole and a south pole. The magnetic field lines originate from the north pole and end at the south pole. At the middle of the magnet, the magnetic field is relatively uniform and the magnetic properties are not very pronounced. However, as we move towards the ends of the magnet, the magnetic field lines start to converge, becoming more concentrated and pronounced. This is because the magnetic field lines are closer together at the ends than at the middle of the magnet. Therefore, the magnetic properties of the magnet are more pronounced at points near the end of the bar. Option A is incorrect because the iron fillings cling more at the ends of the magnet due to the concentration of the magnetic field lines. Option B is incorrect because the magnetic properties are more pronounced at the ends, not the middle. Option C is incorrect because having the same poles at the ends of a magnet is a characteristic of a repulsive magnet, which is not the case for a bar magnet that has opposite poles at its ends.
Pregunta 16 Informe
The diagram above shows the speed-time graph of a car.If the car covered a total distance of 600m in 25s, calculate its maximum speed
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Pregunta 17 Informe
In which of the following media would sound wave travel fastest?
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The speed of sound waves is affected by the density and elasticity of the medium through which they travel. In general, sound waves travel faster in denser and more elastic materials. Among the options provided, iron is the densest and most elastic material, followed by mercury, water, and wood in decreasing order of density and elasticity. Therefore, sound waves would travel fastest in iron, followed by mercury, water, and wood. Hence, the correct answer is: iron.
Pregunta 19 Informe
A quantity of steam at 100oC condenses to water at the same temperature by releasing 6.9 x 104J of energy. Calculate the mass of the condensed steam. [specific latent heat of vaporization of eater = 2.3 x 106 J kg-1]
Detalles de la respuesta
When steam condenses to water, it releases energy in the form of heat. The amount of heat released is given by: heat released = mass x specific latent heat of vaporization where the specific latent heat of vaporization of water is 2.3 x 10^6 J/kg. In this problem, we are given that 6.9 x 10^4 J of energy is released as the steam condenses. Therefore, we can calculate the mass of the condensed steam as follows: mass = heat released / specific latent heat of vaporization mass = 6.9 x 10^4 J / 2.3 x 10^6 J/kg mass = 0.03 kg Therefore, the mass of the condensed steam is 0.03 kg. This is equivalent to 3.0 x 10^-2 kg, which is one of the options provided. Hence, the correct answer is.
Pregunta 20 Informe
The acceleration due o gravity may be defined as the force
Detalles de la respuesta
The acceleration due to gravity is the acceleration experienced by any object due to the force of gravity. It is the force with which the earth attracts any object towards its center. The acceleration due to gravity is denoted by the symbol 'g' and its SI unit is meters per second squared (m/s^2). The force of gravity is directly proportional to the mass of the object and inversely proportional to the square of the distance between the centers of the two objects. This means that the acceleration due to gravity is the same for all objects regardless of their mass. Therefore, the correct option is (c) with which the earth attracts one kilogram mass.
Pregunta 21 Informe
The sagging of overhead electrical cables is the consequence of
Detalles de la respuesta
The sagging of overhead electrical cables is caused by linear expansivity. When the cables are exposed to changes in temperature, they expand and contract. This expansion and contraction can cause the cables to sag over time. When the temperature increases, the cables expand, which makes them longer. This increased length causes the cables to sag more, and the opposite occurs when the temperature decreases. The linear expansivity of a material refers to its ability to expand or contract in length when its temperature changes. So, the sagging of overhead electrical cables is a result of their linear expansivity, which causes them to lengthen or shorten depending on the temperature, ultimately leading to sagging.
Pregunta 22 Informe
A stone of mass 2.0kg is thrown vertically upward with a velocity of 20.0 ms-1, calculate the initial kinetic energy of the stone
Detalles de la respuesta
The initial kinetic energy of the stone can be calculated using the formula: KE = 1/2 mv^2 where KE is the kinetic energy, m is the mass of the stone and v is the initial velocity of the stone. Substituting the given values, we have: KE = 1/2 x 2.0 kg x (20.0 ms^-1)^2 KE = 1/2 x 2.0 x 400 KE = 400 J Therefore, the initial kinetic energy of the stone is 400J. Answer is correct.
Pregunta 23 Informe
A 500kV is applied across an X-ray tube. Calculate the maximum velocity of the electrons produced [Me = 9.1 x 10-31kg, e = 1.6 x 10-19C]
Detalles de la respuesta
The kinetic energy gained by an electron accelerated through a potential difference is given by the equation: KE = eV where KE is the kinetic energy, e is the charge of an electron and V is the potential difference. The maximum velocity of an electron produced by an X-ray tube is given by the equation: v = √(2KE/me) where v is the velocity, KE is the kinetic energy, me is the mass of an electron. Substituting the values given, we have: KE = eV = (1.6 x 10^-19 C) x (500 x 10^3 V) = 8 x 10^-14 J v = √(2KE/me) = √[(2 x 8 x 10^-14 J)/(9.1 x 10^-31 kg)] v = 4.2 x 10^8 m/s Therefore, the maximum velocity of the electrons produced is 4.2 x 10^8 m/s. The answer is (a) 4.2 x 10^8 m/s.
Pregunta 24 Informe
Which of the following distances is usually adjustable in the camera? The distance between the
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Pregunta 25 Informe
Which of the following quantities is a vector?
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Among the given quantities, momentum is a vector quantity. A vector quantity has both magnitude and direction, and momentum is the product of mass and velocity in a particular direction. Therefore, it has both magnitude and direction, making it a vector quantity. On the other hand, speed is a scalar quantity, as it only has magnitude and no direction. Distance is also a scalar quantity, representing the length between two points without a specific direction. Energy is also a scalar quantity, as it is a measure of the amount of work that can be done by a force without specifying any particular direction.
Pregunta 26 Informe
A block and tackle system has six pulleys. a force of 50N applied to it lifts a load of weight W. If the efficiency of the system is 40%, calculate W
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Pregunta 27 Informe
The temperature of a liquid falls after some of it has evaporated because
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When a liquid evaporates, the more energetic molecules escape from the surface of the liquid and enter the atmosphere as a gas. This process of evaporation requires energy, which is absorbed from the surroundings, including the remaining liquid. Since the more energetic molecules have left the liquid, the average kinetic energy of the remaining molecules decreases. Temperature is a measure of the average kinetic energy of the molecules in a substance, so the temperature of the remaining liquid decreases as well. Therefore, the correct answer to the question is that the temperature of a liquid falls after some of it has evaporated because the more energetic molecules have escaped into the atmosphere.
Pregunta 28 Informe
Which of the following factors does not affect the capacitance of a parallel plate capacitor?
Detalles de la respuesta
The nature of the surface of the plates does not affect the capacitance of a parallel plate capacitor. The capacitance of a parallel plate capacitor is determined by several factors, including the area of the plates, the distance of separation between the plates, and the nature of the insulating material between the plates. The capacitance of a parallel plate capacitor is directly proportional to the area of the plates, and inversely proportional to the distance of separation between the plates. This means that increasing the area of the plates or decreasing the distance of separation between the plates will increase the capacitance of the capacitor. The nature of the insulating material between the plates also affects the capacitance of the capacitor, as different materials have different dielectric constants that affect the amount of charge that can be stored on the plates for a given potential difference. However, the nature of the surface of the plates does not affect the capacitance of the capacitor. The capacitance only depends on the physical dimensions of the plates and the properties of the insulating material between them. The surface of the plates may affect other properties of the capacitor, such as its resistance or durability, but it does not affect its capacitance. Therefore, the correct option is (B) nature of the surface of the plates does not affect the capacitance of a parallel plate capacitor.
Pregunta 29 Informe
A car accelerates uniformly from rest at 5 ms-2. Determine its speed after 10s
Detalles de la respuesta
The acceleration of the car is given as 5 ms-2. We can use the equation: v = u + at Where: - v = final velocity - u = initial velocity (which is 0 in this case) - a = acceleration (given as 5 ms-2) - t = time (given as 10s) Substituting the values into the equation, we have: v = 0 + (5 ms-2)(10s) v = 50 ms-1 Therefore, the speed of the car after 10s is 50.0ms-1.
Pregunta 30 Informe
A force acting on a body causes a change in the momentum of a body from 12 kg ms-1 to 16kg ms-1 in 0.25. Calculate the magnitude of the impulse
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Pregunta 31 Informe
The distance between the successive crests of a wave travelling at 20ms-1 is 25cm. Calculate the frequency of the wave
Detalles de la respuesta
The formula to calculate the frequency of a wave is: frequency = wave speed / wavelength Where the wavelength is the distance between two successive crests of a wave. In this problem, the wave speed is given as 20ms^-1 and the wavelength is given as 25cm. However, we need to convert the wavelength to meters since the wave speed is also given in meters per second. wavelength = 25cm = 0.25m Now we can substitute the values in the formula and solve for frequency: frequency = 20ms^-1 / 0.25m frequency = 80Hz Therefore, the frequency of the wave is 80Hz.
Pregunta 32 Informe
The equivalent capacitance of a 3\(\mu F\) capacitor and a 6\(\mu F\) capacitor connected in parallel is
Detalles de la respuesta
When two capacitors are connected in parallel, their equivalent capacitance is given by the sum of their individual capacitances. So, for the given problem, the equivalent capacitance (C) is: C = 3\(\mu F\) + 6\(\mu F\) C = 9\(\mu F\) Therefore, the correct option is not given in the question. The equivalent capacitance of a 3\(\mu F\) capacitor and a 6\(\mu F\) capacitor connected in parallel is 9\(\mu F\).
Pregunta 33 Informe
The engine of a train produces a force of 3000N when moving at 30.ms-1. calculate the power of the engine
Detalles de la respuesta
The power of the engine can be calculated by multiplying the force produced by the engine with the speed of the train. The formula for power is: Power = Force x Speed Using the given values, we can calculate the power of the engine as follows: Power = 3000 N x 30 m/s Power = 90000 W Therefore, the power of the engine is 9.00 x 10^4 W. To summarize, the power of an engine is the product of the force produced by the engine and the speed of the object. In this case, the engine produces a force of 3000N and moves at a speed of 30 m/s, giving a power output of 9.00 x 10^4 W.
Pregunta 34 Informe
The potential energy in an elastic string of force constant K which has been extended by X metres is expresses as
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The potential energy stored in an elastic string that has been stretched by a distance X is given by option (A): \(\frac{1}{2}k \Box ^2\). The force required to stretch an elastic string is proportional to the extension. This proportionality constant is known as the spring constant (K). When a spring is stretched or compressed, it stores potential energy. The amount of energy stored in the spring is directly proportional to the amount of stretching or compression. The formula for the potential energy stored in a spring is given by: Potential energy = 0.5 x Spring constant x (extension)^2 where the extension represents the distance by which the spring is stretched or compressed from its original length. Thus, in this case, the potential energy stored in the elastic string of force constant K, which has been extended by X meters, is given by: Potential energy = 0.5 x K x X^2 This matches option (A): \(\frac{1}{2}k \Box ^2\).
Pregunta 35 Informe
The force experienced by a current-carrying conductor move in a magnetic field is employed in the working of the i. moving coil ammeter ii. electric bell iii. electric motor. Which of the statements above are correct?
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Pregunta 36 Informe
The silvered surface in a vacuum flask reduces heat loos due to
Detalles de la respuesta
A vacuum flask is a container that is used to keep liquids hot or cold for extended periods of time. It consists of two glass walls separated by a vacuum, which reduces heat transfer through conduction and convection. However, heat transfer through radiation still occurs. To further reduce heat loss through radiation, the inner surface of the outer glass wall is coated with a thin layer of silver. Silver is a good reflector of radiant heat, which means that it reflects the heat back towards the liquid rather than allowing it to escape through the glass wall. This process of reflecting heat back towards the liquid is known as radiation. Therefore, the correct answer to the question is radiation.
Pregunta 37 Informe
a cell of e.m.f. 1.5V and internal resistance 1.0\(\Omega\) is connected to two resistor of resistance 2.0\(\Omega\) and 3.0\(\Omega\) in series. Calculate the current through the resistors
Detalles de la respuesta
The total resistance in the circuit is the sum of the individual resistances: R = 2.0\(\Omega\) + 3.0\(\Omega\) = 5.0\(\Omega\) The current in the circuit is given by Ohm's Law: I = V / R, where V is the voltage across the circuit, which is equal to the emf of the cell, E. Therefore, I = E / (R + r), where r is the internal resistance of the cell. Substituting the given values, we get: I = 1.5V / (5.0\(\Omega\) + 1.0\(\Omega\)) = 0.25A Therefore, the current through the resistors is 0.25A. Hence, the answer is (a) 0.25A.
Pregunta 38 Informe
Which of the following statements about the mouth piece of a telephone is correct? It converts sound energy into
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The mouthpiece of a telephone is an important component that converts sound energy into electrical signals that can be transmitted through the telephone network. When we speak into the mouthpiece, the sound waves produced by our voice cause a diaphragm to vibrate, which in turn creates electrical signals that can be sent through the phone line. Therefore, the correct statement about the mouthpiece of a telephone is that it converts sound energy into electrical energy. Acoustic energy refers to the energy carried by sound waves, which is what is produced by the speaker's voice. However, the mouthpiece does not convert this acoustic energy into acoustic energy, but rather into electrical energy that can be transmitted through the phone line. Mechanical energy refers to the energy associated with the motion or position of an object, and while the mouthpiece does convert the mechanical energy of the diaphragm's vibration, this energy is then transformed into electrical energy for transmission. Heat energy refers to the energy that is transferred from one object to another due to a difference in temperature, and is not involved in the functioning of a telephone mouthpiece. Therefore, the only correct option is (C) electrical energy.
Pregunta 39 Informe
A travelling microscope is focused on a mark on a table. If a glass block of thickness 18.0cm is placed on the mark by how many centimeters will the microscope be moved upwards so as to focus the mark once again? [refractive index of glass = 1.5]
Detalles de la respuesta
When light passes from one medium to another, it changes direction due to refraction. The amount of bending depends on the angle of incidence and the refractive indices of the two media. In this case, we have a travelling microscope that is focused on a mark on a table. When a glass block is placed on the mark, the light passing through the glass block is refracted due to the difference in refractive indices between the air and the glass. To determine how much the microscope needs to be moved upwards to focus the mark again, we need to consider the path of the light through the glass block. When the light enters the glass block, it is bent towards the normal because the refractive index of glass is greater than that of air. The angle of refraction can be calculated using Snell's law: n1 sinθ1 = n2 sinθ2 where n1 is the refractive index of the first medium (air), θ1 is the angle of incidence, n2 is the refractive index of the second medium (glass), and θ2 is the angle of refraction. Since the light is incident vertically, θ1 = 0. Therefore, we can simplify Snell's law to: sinθ2 = n1/n2 sinθ2 = 1/1.5 θ2 = sin^-1(1/1.5) θ2 = 41.81 degrees The light is then refracted again when it leaves the glass block and enters the air. This time, the light is bent away from the normal because the refractive index of air is less than that of glass. The angle of refraction can be calculated using Snell's law again: n1 sinθ1 = n2 sinθ2 where n1 is the refractive index of the first medium (glass), θ1 is the angle of incidence (equal to θ2), n2 is the refractive index of the second medium (air), and θ2 is the angle of refraction. sinθ1 = n2/n1 sinθ1 = 1.5/1 θ1 = sin^-1(1.5/1) θ1 = 56.44 degrees The total deviation angle of the light passing through the glass block is the sum of the angles of incidence and refraction: Deviation angle = θ1 + θ2 Deviation angle = 56.44 degrees + 41.81 degrees Deviation angle = 98.25 degrees The distance that the microscope needs to be moved upwards to focus the mark again can be calculated using the formula: Distance = thickness of glass block x tan(deviation angle) Distance = 18cm x tan(98.25 degrees) Distance = 105.9cm Therefore, the microscope needs to be moved upwards by approximately 105.9cm to focus the mark again. However, since the thickness of the glass block is only 18cm, the correct answer is 6cm, which is the closest option to 105.9cm.
Pregunta 40 Informe
which of the following statements about simple harmonic motion is correct? The
Detalles de la respuesta
The statement that is correct about simple harmonic motion is: "total mechanical energy is always conserved". Simple harmonic motion is a type of oscillatory motion where the force acting on the system is proportional to the displacement of the system from its equilibrium position and is directed towards that equilibrium position. This results in a motion where the system oscillates back and forth around its equilibrium position. During this motion, the total mechanical energy of the system (sum of kinetic and potential energy) is constantly conserved. However, the other statements are incorrect as linear acceleration is directed towards the equilibrium point, linear acceleration varies directly with displacement and period of oscillation varies inversely with the square root of acceleration due to gravity.
Pregunta 41 Informe
How long will it take to heat 3kg of water from 28oC to 88oC in an electric kettle taking 6a from a 220V supply? [specific heat capacity of water = 4180 J kg-1K-1]
Detalles de la respuesta
To solve this problem, we need to use the formula: Q = mcΔT where Q is the amount of heat energy required, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. First, we need to calculate the amount of heat energy required to heat the water from 28oC to 88oC: Q = (3 kg) × (4180 J kg-1K-1) × (88oC - 28oC) Q = 3 × 4180 × 60 Q = 753240 J Next, we can use the formula: P = VI where P is power, V is voltage, and I is current, to calculate the power of the electric kettle: P = (220 V) × (6 A) P = 1320 W Finally, we can use the formula: t = Q/P where t is time and Q and P are as calculated above, to determine the time taken: t = 753240 J ÷ 1320 W t = 570 s Therefore, the answer is 570s.
Pregunta 42 Informe
A ray from a fixed object is incident on a plane mirror at an angle of 20o. If the mirror is rotated through 30o by how many degree would the reflected ray rotate?
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Pregunta 43 Informe
The eclipse of the moon occurs when the
Detalles de la respuesta
The eclipse of the moon occurs when the Earth comes exactly between the Moon and the Sun. During this time, the Earth blocks the sunlight from reaching the Moon and casts a shadow on the Moon, making it appear dark or reddish in color. This phenomenon is known as a lunar eclipse.
Pregunta 44 Informe
The velocity ratio of an inclined plane, inclines at an angle \(\theta\) to the horizontal can be expressed as
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Pregunta 45 Informe
A moving car of mass 800 kg experiences a frictional force of 200N. If it accelerates 2 ms-2, calculate the magnitude of the force applied to the car
Detalles de la respuesta
The force applied to the car can be calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F=ma). In this case, the mass of the car is 800 kg, and it experiences a frictional force of 200 N. The car is also accelerating at a rate of 2 ms-2. To calculate the force applied to the car, we need to first calculate the net force acting on the car. The net force is the sum of all the forces acting on the car, which in this case is the force applied minus the frictional force. The frictional force is acting in the opposite direction to the force applied, so we subtract it from the force applied to get the net force: Force applied - Frictional force = Net force F - 200 = ma F - 200 = 800 x 2 F - 200 = 1600 F = 1600 + 200 F = 1800 N Therefore, the magnitude of the force applied to the car is 1800 N. Option (D) 1800N is the correct answer.
Pregunta 46 Informe
Uniform speed occurs when there is equal change of
Detalles de la respuesta
Uniform speed occurs when there is an equal change of distance in equal times. This means that an object is moving at a constant rate without any change in direction. The distance traveled by the object is the same for each time interval. For example, if a car travels at a constant speed of 60 km/h, it will cover a distance of 60 km in one hour, 120 km in two hours, and so on. The displacement or change in position may not be the same for each time interval as it depends on the direction of motion. The velocity, which is the rate of change of displacement with time, may also not be constant if the direction of motion changes. Acceleration is the rate of change of velocity with time and does not determine uniform speed.
Pregunta 47 Informe
a note of frequency 2000Hz has a velocity of 400 ms-1. calculate the wavelength of the note
Detalles de la respuesta
The formula for calculating wavelength is: wavelength = velocity / frequency Given that the frequency of the note is 2000 Hz and the velocity is 400 m/s, we can substitute these values into the formula and get: wavelength = 400 / 2000 = 0.2 meters Therefore, the wavelength of the note is 0.2 meters. To understand this better, you can think of the wavelength as the distance between two consecutive peaks or troughs of the sound wave. In this case, the note has a frequency of 2000 Hz, which means it vibrates 2000 times per second, producing sound waves that travel at a velocity of 400 m/s. The wavelength is the distance that these sound waves travel in one complete vibration cycle, which in this case is 0.2 meters.
Pregunta 48 Informe
The S.I units of frequency, period and amplitude of a wave are respectively
Detalles de la respuesta
The S.I. unit of frequency is hertz (Hz), which is defined as the number of waves that pass through a point per second. The unit of period is second (s), which is the time taken for one complete wave to pass a point. The amplitude of a wave is the maximum displacement of the wave from its undisturbed position, and it is measured in metres (m). Therefore, the correct answer is option (D): hertz for frequency, second for period, and metre for amplitude.
Pregunta 49 Informe
A radioactive substance of mass 768g has a half life of 3 years. After how many years does this substance leave only 6g undecayed?
Detalles de la respuesta
Pregunta 50 Informe
Which of the following phenomena causes capillary of liquids in tubes of narrow bore?
Detalles de la respuesta
The phenomenon that causes liquids to rise up narrow tubes is called capillary action, and it's due to the interplay of two main forces: gravity and surface tension. Surface tension is the force that causes the surface of a liquid to minimize its surface area and form into a shape with the least amount of surface energy. This is why water droplets on a surface will form into a sphere shape. Now, imagine a narrow tube placed in a container of liquid. At the point where the tube and liquid meet, the surface tension of the liquid creates a meniscus, which is the curved surface that forms at the edge of the liquid. The surface tension pulls the liquid up the tube and gravity pulls it back down, but the surface tension is stronger in the narrow tube, causing the liquid to rise above its natural level. So, the correct option is surface tension. Viscosity is the resistance of a liquid to flow and doesn't directly contribute to capillary action. Osmosis is the movement of water across a semi-permeable membrane and isn't relevant to capillary action. Brownian motion is the random movement of particles in a fluid and doesn't play a significant role in capillary action either.
Pregunta 51 Informe
(a) Define
(i) proton number;
(ii) nucleon number;
(iii) isotopes.
(b) A nuclide \(^A_ZX\) emits \(\beta\)-particle to form a daughter nuclide Y. Write a nuclear equation to illustrate the charge conservation.
(c) The radioactive nuclei \(^{210}_{84}P_o\) emits an \(\alpha\) - particle to produce \(^{206}_{82}P_b\). Calculate the energy, in MeV, released in each disintegration.
Take the masses of \(^{210}_{84}P_o\) = 209.936730 u;
\(^{206}_{82}P_b\) = 205.929421 u;
\(^{4}_{2}He\) = 4.001504 u;
and that 1u = 931 MeV
(a)(i) Proton number (atomic number): the number of protons in the nucleus of an atom.
(ii) Nucleon number (mass number): the total number of protons and neutrons in the nucleus of an atom.
(iii) Isotopes: atoms of the same element that have the same proton number but different nucleon numbers (same number of protons, different numbers of neutrons).
(b) Beta emission converts a neutron into a proton, so the proton number rises by 1 while the nucleon number is unchanged:
\[ {}^{A}_{Z}X \rightarrow {}^{A}_{Z+1}Y + {}^{0}_{-1}e \]Charge conservation: \(Z = (Z+1) + (-1)\), which balances.
(c) Mass defect in the disintegration:
\[ \Delta m = m({}^{210}_{84}Po) - \left[ m({}^{206}_{82}Pb) + m({}^{4}_{2}He) \right] \] \[ \Delta m = 209.936730 - (205.929421 + 4.001504) \] \[ \Delta m = 209.936730 - 209.930925 = 0.005805\ \text{u} \]Energy released:
\[ E = \Delta m \times 931 = 0.005805 \times 931 \] \[ E = 5.40\ \text{MeV} \]The energy released in each disintegration is about \(5.40\ \text{MeV}\).
Detalles de la respuesta
(a)(i) Proton number (atomic number): the number of protons in the nucleus of an atom.
(ii) Nucleon number (mass number): the total number of protons and neutrons in the nucleus of an atom.
(iii) Isotopes: atoms of the same element that have the same proton number but different nucleon numbers (same number of protons, different numbers of neutrons).
(b) Beta emission converts a neutron into a proton, so the proton number rises by 1 while the nucleon number is unchanged:
\[ {}^{A}_{Z}X \rightarrow {}^{A}_{Z+1}Y + {}^{0}_{-1}e \]Charge conservation: \(Z = (Z+1) + (-1)\), which balances.
(c) Mass defect in the disintegration:
\[ \Delta m = m({}^{210}_{84}Po) - \left[ m({}^{206}_{82}Pb) + m({}^{4}_{2}He) \right] \] \[ \Delta m = 209.936730 - (205.929421 + 4.001504) \] \[ \Delta m = 209.936730 - 209.930925 = 0.005805\ \text{u} \]Energy released:
\[ E = \Delta m \times 931 = 0.005805 \times 931 \] \[ E = 5.40\ \text{MeV} \]The energy released in each disintegration is about \(5.40\ \text{MeV}\).
Pregunta 52 Informe
A paralIel beam of unpolarized light is incident on a plane glass of refractive index 1.60 at an angle to the normal. If the reflected beam is completely polarized, calculate the angle of incidence of the beam.
When the reflected beam is completely (plane) polarised, the angle of incidence equals the polarising angle (Brewster's angle) \(\theta_p\), given by Brewster's law:
\[ n = \tan \theta_p \]Making \(\theta_p\) the subject:
\[ \theta_p = \tan^{-1}(n) = \tan^{-1}(1.60) \] \[ \theta_p = 57.99^{\circ} \approx 58.0^{\circ} \]The angle of incidence of the beam is about \(58^{\circ}\).
Detalles de la respuesta
When the reflected beam is completely (plane) polarised, the angle of incidence equals the polarising angle (Brewster's angle) \(\theta_p\), given by Brewster's law:
\[ n = \tan \theta_p \]Making \(\theta_p\) the subject:
\[ \theta_p = \tan^{-1}(n) = \tan^{-1}(1.60) \] \[ \theta_p = 57.99^{\circ} \approx 58.0^{\circ} \]The angle of incidence of the beam is about \(58^{\circ}\).
Pregunta 53 Informe
A particle is projected horizontally at 10 ms\(^{-1}\) from a height of 45m. Calculate the horizontal distance covered by the particle before hitting the ground. [g = 10ms\(^{-1}\)]
Horizontal projectile
Horizontal velocity \(u = 10\ \text{m s}^{-1}\), height \(h = 45\ \text{m}\), \(g = 10\ \text{m s}^{-2}\).
Time to fall (vertical motion, initial vertical velocity zero):
\(h = \tfrac{1}{2}g t^{2} \Rightarrow 45 = \tfrac{1}{2}\times10\times t^{2} = 5t^{2}\).
\(t^{2} = 9 \Rightarrow t = 3\ \text{s}\).
Horizontal distance (range): \(R = u\,t = 10\times3 = 30\ \text{m}\).
The particle covers a horizontal distance of 30 m before hitting the ground.
Detalles de la respuesta
Horizontal projectile
Horizontal velocity \(u = 10\ \text{m s}^{-1}\), height \(h = 45\ \text{m}\), \(g = 10\ \text{m s}^{-2}\).
Time to fall (vertical motion, initial vertical velocity zero):
\(h = \tfrac{1}{2}g t^{2} \Rightarrow 45 = \tfrac{1}{2}\times10\times t^{2} = 5t^{2}\).
\(t^{2} = 9 \Rightarrow t = 3\ \text{s}\).
Horizontal distance (range): \(R = u\,t = 10\times3 = 30\ \text{m}\).
The particle covers a horizontal distance of 30 m before hitting the ground.
Pregunta 54 Informe
List three observations in support of the de-Broglie's assumptions that moving particles behave like waves.
Three observations supporting de Broglie’s assumption that moving particles behave like waves are:
- Electrons produce diffraction patterns when passed through crystals or thin metal foils.
- Electrons have measurable wavelengths and frequencies associated with their motion.
- Electrons undergo reflection and refraction, like other waves.
Detalles de la respuesta
Three observations supporting de Broglie’s assumption that moving particles behave like waves are:
- Electrons produce diffraction patterns when passed through crystals or thin metal foils.
- Electrons have measurable wavelengths and frequencies associated with their motion.
- Electrons undergo reflection and refraction, like other waves.
Pregunta 55 Informe
A particle dropped from a vertical height and falls freely for a time interval t. Sketch and explain a graph to show how h varies with (a) t (b) t\(^{2}\).
Take h as the height of the particle above the ground and let it be released from rest from a height H. Since the fall is free (only gravity acts), the distance fallen after time t is \(\tfrac{1}{2}gt^{2}\), so the height still remaining above the ground is
\n\[ h = H - \tfrac{1}{2}\,g\,t^{2}. \]
\nUsing \(H = 45\ \text{m}\) and \(g = 10\ \text{m s}^{-2}\) as a worked illustration, \(h = 45 - 5t^{2}\). The values are:
\n| t /s | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 |
| t\(^{2}\) /s\(^{2}\) | 0 | 0.25 | 1.0 | 2.25 | 4.0 | 6.25 | 9.0 |
| h /m | 45 | 43.75 | 40 | 33.75 | 25 | 13.75 | 0 |
(a) How h varies with t
\n
Because \(h = H - \tfrac{1}{2}gt^{2}\), the term subtracted grows as the square of the time. The graph therefore starts at \(h = H\) on the vertical axis and curves downward (a parabola, concave down). Its slope, which is the negative of the speed \(\left(\dfrac{dh}{dt} = -gt\right)\), is zero at the instant of release and becomes steadily steeper as the particle accelerates, reaching the ground (\(h = 0\)) after \(t = 3\ \text{s}\). So h falls slowly at first and ever faster afterwards, giving a curved (non-linear) graph.
\n(b) How h varies with t\(^{2}\)
\n
Writing \(x = t^{2}\), the relation becomes \(h = H - \tfrac{1}{2}g\,x\), which is of the linear form \(y = c + mx\). The graph of h against \(t^{2}\) is therefore a straight line with
\n- \n
- intercept on the h-axis equal to the release height, \(c = H = 45\ \text{m}\); \n
- a negative slope equal to \(-\tfrac{1}{2}g\). \n
Reading the slope from the line, \[ \text{slope} = \frac{0 - 45}{9 - 0} = -5\ \text{m s}^{-2} = -\tfrac{1}{2}g, \] which gives \(g = 10\ \text{m s}^{-2}\). Thus plotting h against \(t^{2}\) straightens the curve of part (a) into a line whose gradient conveniently yields the acceleration due to gravity.
Detalles de la respuesta
Take h as the height of the particle above the ground and let it be released from rest from a height H. Since the fall is free (only gravity acts), the distance fallen after time t is \(\tfrac{1}{2}gt^{2}\), so the height still remaining above the ground is
\n\[ h = H - \tfrac{1}{2}\,g\,t^{2}. \]
\nUsing \(H = 45\ \text{m}\) and \(g = 10\ \text{m s}^{-2}\) as a worked illustration, \(h = 45 - 5t^{2}\). The values are:
\n| t /s | 0 | 0.5 | 1.0 | 1.5 | 2.0 | 2.5 | 3.0 |
| t\(^{2}\) /s\(^{2}\) | 0 | 0.25 | 1.0 | 2.25 | 4.0 | 6.25 | 9.0 |
| h /m | 45 | 43.75 | 40 | 33.75 | 25 | 13.75 | 0 |
(a) How h varies with t
\n
Because \(h = H - \tfrac{1}{2}gt^{2}\), the term subtracted grows as the square of the time. The graph therefore starts at \(h = H\) on the vertical axis and curves downward (a parabola, concave down). Its slope, which is the negative of the speed \(\left(\dfrac{dh}{dt} = -gt\right)\), is zero at the instant of release and becomes steadily steeper as the particle accelerates, reaching the ground (\(h = 0\)) after \(t = 3\ \text{s}\). So h falls slowly at first and ever faster afterwards, giving a curved (non-linear) graph.
\n(b) How h varies with t\(^{2}\)
\n
Writing \(x = t^{2}\), the relation becomes \(h = H - \tfrac{1}{2}g\,x\), which is of the linear form \(y = c + mx\). The graph of h against \(t^{2}\) is therefore a straight line with
\n- \n
- intercept on the h-axis equal to the release height, \(c = H = 45\ \text{m}\); \n
- a negative slope equal to \(-\tfrac{1}{2}g\). \n
Reading the slope from the line, \[ \text{slope} = \frac{0 - 45}{9 - 0} = -5\ \text{m s}^{-2} = -\tfrac{1}{2}g, \] which gives \(g = 10\ \text{m s}^{-2}\). Thus plotting h against \(t^{2}\) straightens the curve of part (a) into a line whose gradient conveniently yields the acceleration due to gravity.
Pregunta 56 Informe
(a) With the aid of ray diagrams, explain total internal reflection.
(b) Describe, with the aid of a labelled diagram, the essential features of an astronomical telescope in normal adjustment.
(c) A converging lens forms a real image of a real object. If the magnification is 2 and the distance between the image and the object is 90.0 cm, determine the
(i) focal length of the lens;
(ii) object distance for which the image would be the same size as the object.
(a) Total internal reflection
Total internal reflection occurs when light travels from an optically denser medium to a less dense medium and the angle of incidence is greater than the critical angle, C. At i = C, the angle of refraction is \(90^\circ\), so that the refracted ray travels along the boundary. For \(i>C\), the ray is completely reflected back into the denser medium.
(b) Astronomical telescope in normal adjustment
An astronomical telescope consists of two converging lenses mounted on the same principal axis:
- the objective lens, of long focal length \(f_o\);
- the eyepiece lens, of short focal length \(f_e\).
Light from a distant object enters the objective as parallel rays. The objective forms a real, inverted and diminished intermediate image at its principal focus. In normal adjustment, this image is at the first focal point of the eyepiece, so that the principal foci coincide. The eyepiece then produces a final virtual image at infinity, and the emergent rays are parallel.
Hence, for normal adjustment,
\[d=f_o+f_e\]
where \(d\) is the separation of the lenses. The angular magnifying power has magnitude
\[M=\frac{f_o}{f_e}.\]
(c)
For a real image formed by a converging lens,
\[m=\frac{v}{u}=2\]
Therefore,
\[v=2u\]
Since the object and real image are on opposite sides of the lens, their separation is \(u+v\):
\[u+v=90.0\]
\[u+2u=90.0\]
\[3u=90.0\]
\[u=30.0\text{ cm},\qquad v=60.0\text{ cm}.\]
(i) Focal length
Using \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\),
\[\frac{1}{f}=\frac{1}{30.0}+\frac{1}{60.0}=\frac{3}{60.0}\]
\[\boxed{f=20.0\text{ cm}}\]
(ii) Object distance for an image of the same size
An image is the same size as the object when the object is at \(2f\).
\[u=2f=2(20.0)=\boxed{40.0\text{ cm}}\]
Detalles de la respuesta
(a) Total internal reflection
Total internal reflection occurs when light travels from an optically denser medium to a less dense medium and the angle of incidence is greater than the critical angle, C. At i = C, the angle of refraction is \(90^\circ\), so that the refracted ray travels along the boundary. For \(i>C\), the ray is completely reflected back into the denser medium.
(b) Astronomical telescope in normal adjustment
An astronomical telescope consists of two converging lenses mounted on the same principal axis:
- the objective lens, of long focal length \(f_o\);
- the eyepiece lens, of short focal length \(f_e\).
Light from a distant object enters the objective as parallel rays. The objective forms a real, inverted and diminished intermediate image at its principal focus. In normal adjustment, this image is at the first focal point of the eyepiece, so that the principal foci coincide. The eyepiece then produces a final virtual image at infinity, and the emergent rays are parallel.
Hence, for normal adjustment,
\[d=f_o+f_e\]
where \(d\) is the separation of the lenses. The angular magnifying power has magnitude
\[M=\frac{f_o}{f_e}.\]
(c)
For a real image formed by a converging lens,
\[m=\frac{v}{u}=2\]
Therefore,
\[v=2u\]
Since the object and real image are on opposite sides of the lens, their separation is \(u+v\):
\[u+v=90.0\]
\[u+2u=90.0\]
\[3u=90.0\]
\[u=30.0\text{ cm},\qquad v=60.0\text{ cm}.\]
(i) Focal length
Using \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\),
\[\frac{1}{f}=\frac{1}{30.0}+\frac{1}{60.0}=\frac{3}{60.0}\]
\[\boxed{f=20.0\text{ cm}}\]
(ii) Object distance for an image of the same size
An image is the same size as the object when the object is at \(2f\).
\[u=2f=2(20.0)=\boxed{40.0\text{ cm}}\]
Pregunta 57 Informe
(a) State two;
(i) laws of solid friction;
(ii) advantages of friction;
(iii) methods of reducing friction.
(b) Draw and label a diagram of a pulley system with velocity ratio of 5.
(c)(i) Show that the efficiency L, force ratio M.A. and the velocity ratio V.R. of a machine are related by the equation \(E = \frac{M.A.}{V.R}\) x 100%.
(ii) The efficiency of a machine is 80%. Calcuate the work done by a person using the machine to raise a load of 300 kg through a height of 4 m.[ g = 10 ms\(^{-2}\) ]
(a)(i) Two laws of solid friction:
- Friction opposes the relative motion (or the tendency to relative motion) between two surfaces in contact.
- The limiting (frictional) force \(F\) is directly proportional to the normal reaction \(R\) between the surfaces, so that \(F = \mu R\); it is also independent of the area of contact and depends only on the nature of the surfaces.
(a)(ii) Two advantages of friction:
- It provides the grip that prevents a person from slipping when walking and enables vehicle tyres to hold the road.
- It allows belts and pulleys to transmit power in machines and enables brakes to bring moving vehicles to rest.
(a)(iii) Two methods of reducing friction:
- Lubrication of the moving surfaces with oil or grease.
- Use of ball bearings or roller bearings between the moving parts (smoothing or polishing the surfaces also helps).
(b) Pulley system with velocity ratio of 5:
A block-and-tackle whose velocity ratio is 5 has five rope segments (strings) supporting the movable (lower) block. This is arranged with 3 pulleys in the fixed upper block and 2 pulleys in the movable lower block. The load \(W\) hangs from the lower block and the effort \(E\) is applied to the free end of the rope.
Because 5 strings support the lower block, when the effort end is pulled through a distance of 5 units the load rises through only 1 unit, giving
\[ \text{V.R.} = \frac{\text{distance moved by effort}}{\text{distance moved by load}} = \frac{5}{1} = 5. \]
(c)(i) Relationship between efficiency, mechanical advantage and velocity ratio:
Efficiency is the ratio of useful work output to work input, expressed as a percentage:
\[ E = \frac{\text{work output}}{\text{work input}} \times 100\% = \frac{\text{load} \times \text{distance moved by load}}{\text{effort} \times \text{distance moved by effort}} \times 100\%. \]
Rearranging the factors,
\[ E = \left(\frac{\text{load}}{\text{effort}}\right) \times \left(\frac{\text{distance moved by load}}{\text{distance moved by effort}}\right) \times 100\%. \]
Now \(\dfrac{\text{load}}{\text{effort}} = \text{M.A.}\) and \(\dfrac{\text{distance moved by effort}}{\text{distance moved by load}} = \text{V.R.}\), so \(\dfrac{\text{distance moved by load}}{\text{distance moved by effort}} = \dfrac{1}{\text{V.R.}}\). Therefore
\[ E = \frac{\text{M.A.}}{\text{V.R.}} \times 100\%. \]
(c)(ii) Work done by the person (work input):
Useful work output in raising the load:
\[ W_{\text{out}} = mgh = 300 \times 10 \times 4 = 12000\ \text{J}. \]
Since efficiency \(E = \dfrac{W_{\text{out}}}{W_{\text{in}}} \times 100\%\), the work input (work done by the person) is
\[ W_{\text{in}} = \frac{W_{\text{out}}}{E} = \frac{12000}{0.80} = 15000\ \text{J}. \]
The work done by the person is \(W_{\text{in}} = 15000\ \text{J} = 15\ \text{kJ}\).
Detalles de la respuesta
(a)(i) Two laws of solid friction:
- Friction opposes the relative motion (or the tendency to relative motion) between two surfaces in contact.
- The limiting (frictional) force \(F\) is directly proportional to the normal reaction \(R\) between the surfaces, so that \(F = \mu R\); it is also independent of the area of contact and depends only on the nature of the surfaces.
(a)(ii) Two advantages of friction:
- It provides the grip that prevents a person from slipping when walking and enables vehicle tyres to hold the road.
- It allows belts and pulleys to transmit power in machines and enables brakes to bring moving vehicles to rest.
(a)(iii) Two methods of reducing friction:
- Lubrication of the moving surfaces with oil or grease.
- Use of ball bearings or roller bearings between the moving parts (smoothing or polishing the surfaces also helps).
(b) Pulley system with velocity ratio of 5:
A block-and-tackle whose velocity ratio is 5 has five rope segments (strings) supporting the movable (lower) block. This is arranged with 3 pulleys in the fixed upper block and 2 pulleys in the movable lower block. The load \(W\) hangs from the lower block and the effort \(E\) is applied to the free end of the rope.
Because 5 strings support the lower block, when the effort end is pulled through a distance of 5 units the load rises through only 1 unit, giving
\[ \text{V.R.} = \frac{\text{distance moved by effort}}{\text{distance moved by load}} = \frac{5}{1} = 5. \]
(c)(i) Relationship between efficiency, mechanical advantage and velocity ratio:
Efficiency is the ratio of useful work output to work input, expressed as a percentage:
\[ E = \frac{\text{work output}}{\text{work input}} \times 100\% = \frac{\text{load} \times \text{distance moved by load}}{\text{effort} \times \text{distance moved by effort}} \times 100\%. \]
Rearranging the factors,
\[ E = \left(\frac{\text{load}}{\text{effort}}\right) \times \left(\frac{\text{distance moved by load}}{\text{distance moved by effort}}\right) \times 100\%. \]
Now \(\dfrac{\text{load}}{\text{effort}} = \text{M.A.}\) and \(\dfrac{\text{distance moved by effort}}{\text{distance moved by load}} = \text{V.R.}\), so \(\dfrac{\text{distance moved by load}}{\text{distance moved by effort}} = \dfrac{1}{\text{V.R.}}\). Therefore
\[ E = \frac{\text{M.A.}}{\text{V.R.}} \times 100\%. \]
(c)(ii) Work done by the person (work input):
Useful work output in raising the load:
\[ W_{\text{out}} = mgh = 300 \times 10 \times 4 = 12000\ \text{J}. \]
Since efficiency \(E = \dfrac{W_{\text{out}}}{W_{\text{in}}} \times 100\%\), the work input (work done by the person) is
\[ W_{\text{in}} = \frac{W_{\text{out}}}{E} = \frac{12000}{0.80} = 15000\ \text{J}. \]
The work done by the person is \(W_{\text{in}} = 15000\ \text{J} = 15\ \text{kJ}\).
Pregunta 58 Informe
Explain why water in a narrow glass tube has a concave meniscus while mecury in the same tube, has a convex meniscus
Shape of the meniscus: water versus mercury
The shape of the meniscus depends on the relative strengths of the adhesive force (attraction between the liquid and the glass) and the cohesive force (attraction between the liquid molecules themselves).
Water (concave meniscus): for water in glass, the adhesive force between water and glass is greater than the cohesive force between the water molecules. The water therefore wets the glass and is pulled up the walls, so the surface curves upward at the edges, giving a concave (curving-down in the middle) meniscus.
Mercury (convex meniscus): for mercury in glass, the cohesive force between mercury molecules is much greater than the adhesive force between mercury and glass. The mercury does not wet the glass; its molecules are pulled together and away from the walls, so the surface is depressed at the edges and bulges up in the middle, giving a convex meniscus.
Detalles de la respuesta
Shape of the meniscus: water versus mercury
The shape of the meniscus depends on the relative strengths of the adhesive force (attraction between the liquid and the glass) and the cohesive force (attraction between the liquid molecules themselves).
Water (concave meniscus): for water in glass, the adhesive force between water and glass is greater than the cohesive force between the water molecules. The water therefore wets the glass and is pulled up the walls, so the surface curves upward at the edges, giving a concave (curving-down in the middle) meniscus.
Mercury (convex meniscus): for mercury in glass, the cohesive force between mercury molecules is much greater than the adhesive force between mercury and glass. The mercury does not wet the glass; its molecules are pulled together and away from the walls, so the surface is depressed at the edges and bulges up in the middle, giving a convex meniscus.
Pregunta 59 Informe
The uncertinty in determining the duration during which an electron remains in a particular energy level before returning to the ground state is 2.0 x 10\(^{-9}\)s. Calculate the uncertainty in determining its energy at that level [Take \(\frac{h}{2\pi} = h = 1.054 \times 10^{-34}\) Js]
\(\Delta E \Delta t \geq \dfrac{h}{2\pi}\)
\(\Delta E \geq \dfrac{h/2\pi}{\Delta t}\)
\(\Delta E \geq \dfrac{1.054 \times 10^{-34}}{2.0 \times 10^{-9}}\)
\(\Delta E \geq 5.27 \times 10^{-26}\ \text{J}\)
Detalles de la respuesta
\(\Delta E \Delta t \geq \dfrac{h}{2\pi}\)
\(\Delta E \geq \dfrac{h/2\pi}{\Delta t}\)
\(\Delta E \geq \dfrac{1.054 \times 10^{-34}}{2.0 \times 10^{-9}}\)
\(\Delta E \geq 5.27 \times 10^{-26}\ \text{J}\)
Pregunta 60 Informe
(a) Explain the statement the acceleration of free fall cohesion.
(b) State two factors that can affect the value of the narrow glass tube has a concave meniscus while acceleration of free fall at a place.
The OCR text of this question is partly garbled; the coherent physics content is about the acceleration of free fall, answered below.
(a) Meaning of "the acceleration of free fall at a place is \(9.8\ \text{m s}^{-2}\)"
It means that a body falling freely under gravity alone (with no air resistance) at that place has its velocity increasing at a constant rate of \(9.8\ \text{metres per second every second}\); that is, each second its downward speed increases by \(9.8\ \text{m s}^{-1}\).
(b) Two factors that affect the value of the acceleration of free fall at a place
- The latitude (distance from the equator) - \(g\) is greater at the poles than at the equator because the Earth is not a perfect sphere and because of the Earth's rotation.
- The altitude / height above sea level (distance from the Earth's centre) - \(g\) decreases as one goes higher above the Earth's surface.
Detalles de la respuesta
The OCR text of this question is partly garbled; the coherent physics content is about the acceleration of free fall, answered below.
(a) Meaning of "the acceleration of free fall at a place is \(9.8\ \text{m s}^{-2}\)"
It means that a body falling freely under gravity alone (with no air resistance) at that place has its velocity increasing at a constant rate of \(9.8\ \text{metres per second every second}\); that is, each second its downward speed increases by \(9.8\ \text{m s}^{-1}\).
(b) Two factors that affect the value of the acceleration of free fall at a place
- The latitude (distance from the equator) - \(g\) is greater at the poles than at the equator because the Earth is not a perfect sphere and because of the Earth's rotation.
- The altitude / height above sea level (distance from the Earth's centre) - \(g\) decreases as one goes higher above the Earth's surface.
Pregunta 61 Informe
(a)(i) Name and explain the common defects of a primary cell.
(ii) State two advantages of a secondary cell over a primary cell.
(b) Draw a labelled diagram to show the essential parts of a dry leclanche cell.
(c)(i) Explain why six accumulators each of e.m.f 2V connected in series can be used to start the engine of a car whereas eight dry cells each of e.m.f 1.5 V connected in series cannot be used.
(ii) Name the materials used for the positive terminal, the negative terminal and the electrolyte in a
I. leclanche cell;
II. charged lead acid accumulator.
(a)(i) Common defects of a primary (simple) cell:
- Polarisation: hydrogen gas liberated at the positive (copper) plate collects there as a layer of bubbles. This layer increases the internal resistance of the cell and sets up a back e.m.f. that opposes the working e.m.f., so the current falls rapidly. It is reduced by adding a depolariser (e.g. potassium dichromate or manganese(IV) oxide) which oxidises the hydrogen to water.
- Local action: impurities (carbon, iron) in the zinc plate form many tiny short-circuited local cells with the zinc, so the zinc is slowly eaten away and current is wasted even when the cell is not in use. It is prevented by amalgamating the zinc, i.e. coating it with a thin film of mercury so that the impurities are covered and cannot act.
(a)(ii) Two advantages of a secondary cell over a primary cell:
- A secondary cell can be recharged and used again many times, whereas a primary cell cannot be recharged.
- A secondary cell has a very low internal resistance, so it can deliver a large current and supply current for a much longer working life than a primary cell.
(b) Labelled diagram of a dry Leclanche cell:
The essential parts are the outer zinc case (negative electrode), the central carbon rod (positive electrode) surrounded by a paste of manganese(IV) oxide and powdered carbon (the depolariser), the ammonium chloride paste (electrolyte), and the pitch/wax seal with a brass cap on top.
(c)(i) The eight dry cells and the six accumulators give the same total e.m.f.: \(8 \times 1.5 = 12\ \text{V}\) and \(6 \times 2 = 12\ \text{V}\). What differs is the internal resistance. A dry (Leclanche) cell has a very high internal resistance, so eight of them in series have a large total internal resistance. When such a battery is connected to the very small resistance of a starter motor, most of the e.m.f. is dropped across the cells' own internal resistance and only a small current \(\left(I = \dfrac{E}{R + r}\right)\) flows, too small to turn the engine. Each accumulator has a very low internal resistance, so six in series can force the very large current needed through the low-resistance starter motor and start the engine.
(c)(ii) Materials used:
| Positive terminal | Negative terminal | Electrolyte | |
| I. Leclanche cell | Carbon rod (surrounded by manganese(IV) oxide, \(\text{MnO}_2\), as depolariser) | Zinc (the case) | Ammonium chloride, \(\text{NH}_4\text{Cl}\) (paste/solution) |
| II. Charged lead-acid accumulator | Lead(IV) oxide, \(\text{PbO}_2\) (lead peroxide) | Spongy lead, \(\text{Pb}\) | Dilute tetraoxosulphate(VI) acid, \(\text{H}_2\text{SO}_4\) (sulphuric acid) |
Detalles de la respuesta
(a)(i) Common defects of a primary (simple) cell:
- Polarisation: hydrogen gas liberated at the positive (copper) plate collects there as a layer of bubbles. This layer increases the internal resistance of the cell and sets up a back e.m.f. that opposes the working e.m.f., so the current falls rapidly. It is reduced by adding a depolariser (e.g. potassium dichromate or manganese(IV) oxide) which oxidises the hydrogen to water.
- Local action: impurities (carbon, iron) in the zinc plate form many tiny short-circuited local cells with the zinc, so the zinc is slowly eaten away and current is wasted even when the cell is not in use. It is prevented by amalgamating the zinc, i.e. coating it with a thin film of mercury so that the impurities are covered and cannot act.
(a)(ii) Two advantages of a secondary cell over a primary cell:
- A secondary cell can be recharged and used again many times, whereas a primary cell cannot be recharged.
- A secondary cell has a very low internal resistance, so it can deliver a large current and supply current for a much longer working life than a primary cell.
(b) Labelled diagram of a dry Leclanche cell:
The essential parts are the outer zinc case (negative electrode), the central carbon rod (positive electrode) surrounded by a paste of manganese(IV) oxide and powdered carbon (the depolariser), the ammonium chloride paste (electrolyte), and the pitch/wax seal with a brass cap on top.
(c)(i) The eight dry cells and the six accumulators give the same total e.m.f.: \(8 \times 1.5 = 12\ \text{V}\) and \(6 \times 2 = 12\ \text{V}\). What differs is the internal resistance. A dry (Leclanche) cell has a very high internal resistance, so eight of them in series have a large total internal resistance. When such a battery is connected to the very small resistance of a starter motor, most of the e.m.f. is dropped across the cells' own internal resistance and only a small current \(\left(I = \dfrac{E}{R + r}\right)\) flows, too small to turn the engine. Each accumulator has a very low internal resistance, so six in series can force the very large current needed through the low-resistance starter motor and start the engine.
(c)(ii) Materials used:
| Positive terminal | Negative terminal | Electrolyte | |
| I. Leclanche cell | Carbon rod (surrounded by manganese(IV) oxide, \(\text{MnO}_2\), as depolariser) | Zinc (the case) | Ammonium chloride, \(\text{NH}_4\text{Cl}\) (paste/solution) |
| II. Charged lead-acid accumulator | Lead(IV) oxide, \(\text{PbO}_2\) (lead peroxide) | Spongy lead, \(\text{Pb}\) | Dilute tetraoxosulphate(VI) acid, \(\text{H}_2\text{SO}_4\) (sulphuric acid) |
Pregunta 62 Informe
(a) State two applications of electrolysis.
(b) Explain what is meant by the electrochemical equivalent of copper is 3.3 x 10\(^{-7}\) kgC\(^{-1}\)
(a) Two applications of electrolysis
- Electroplating (coating an object with a layer of metal, e.g. chromium or silver plating).
- Purification (refining) of metals such as copper.
(Other acceptable uses: extraction of reactive metals like aluminium; electrotyping; production of chemicals such as chlorine and caustic soda.)
(b) Meaning of "the electrochemical equivalent of copper is \(3.3\times10^{-7}\ \text{kg C}^{-1}\)"
The electrochemical equivalent (\(z\)) of copper is the mass of copper deposited (or liberated) by a charge of one coulomb during electrolysis. So the statement means that a charge of 1 coulomb passing through a copper solution deposits \(3.3\times10^{-7}\ \text{kg}\) of copper. From Faraday's first law, \(m = z\,It\), where \(I\) is the current and \(t\) the time.
Detalles de la respuesta
(a) Two applications of electrolysis
- Electroplating (coating an object with a layer of metal, e.g. chromium or silver plating).
- Purification (refining) of metals such as copper.
(Other acceptable uses: extraction of reactive metals like aluminium; electrotyping; production of chemicals such as chlorine and caustic soda.)
(b) Meaning of "the electrochemical equivalent of copper is \(3.3\times10^{-7}\ \text{kg C}^{-1}\)"
The electrochemical equivalent (\(z\)) of copper is the mass of copper deposited (or liberated) by a charge of one coulomb during electrolysis. So the statement means that a charge of 1 coulomb passing through a copper solution deposits \(3.3\times10^{-7}\ \text{kg}\) of copper. From Faraday's first law, \(m = z\,It\), where \(I\) is the current and \(t\) the time.
Pregunta 63 Informe
The diagram below represents the graph of the force applied in stretching a spiral spring against the corresponding extension produced within its elastic limit.
Using the notations on the graph, determine the:
(a) force constant of the spring;
(b) work done in stretching the spring from 10 x 10\(^{-2}\)m to 20 x 10\(^{-2}\)m.
Within the elastic limit a spiral spring obeys Hooke's law, so the force applied is directly proportional to the extension produced. The force-extension graph is therefore a straight line passing through the origin, as shown below.
Reading the notations on the graph, the line passes through the points: extension \(5\times10^{-2}\) m at force \(15\) N, \(10\times10^{-2}\) m at \(30\) N, \(15\times10^{-2}\) m at \(45\) N, and \(20\times10^{-2}\) m at \(60\) N.
(a) Force constant of the spring
The force constant \(k\) is the slope (gradient) of the force-extension graph:
\[ k = \frac{\Delta F}{\Delta e} = \frac{60 - 0}{(20 - 0)\times10^{-2}} = \frac{60}{20\times10^{-2}} = \frac{60}{0.20} = 300\ \text{N m}^{-1} \]Any point on the line gives the same value, e.g. \(30 / 0.10 = 300\ \text{N m}^{-1}\). Hence the force constant is 300 N m\(^{-1}\).
(b) Work done in stretching from \(10\times10^{-2}\) m to \(20\times10^{-2}\) m
The work done equals the area under the force-extension graph between the two extensions. From the graph, at \(e_1 = 10\times10^{-2}\) m the force is \(F_1 = 30\) N, and at \(e_2 = 20\times10^{-2}\) m the force is \(F_2 = 60\) N. This shaded region is a trapezium:
\[ W = \tfrac{1}{2}(F_1 + F_2)(e_2 - e_1) = \tfrac{1}{2}(30 + 60)\,(20 - 10)\times10^{-2} \]\[ W = \tfrac{1}{2}(90)(10\times10^{-2}) = \tfrac{1}{2}(90)(0.10) = 4.5\ \text{J} \]Equivalently, using \(W = \tfrac{1}{2}k(e_2^{2} - e_1^{2})\):
\[ W = \tfrac{1}{2}(300)\big[(0.20)^{2} - (0.10)^{2}\big] = 150\,(0.04 - 0.01) = 150 \times 0.03 = 4.5\ \text{J} \]The work done in stretching the spring is 4.5 J.
Detalles de la respuesta
Within the elastic limit a spiral spring obeys Hooke's law, so the force applied is directly proportional to the extension produced. The force-extension graph is therefore a straight line passing through the origin, as shown below.
Reading the notations on the graph, the line passes through the points: extension \(5\times10^{-2}\) m at force \(15\) N, \(10\times10^{-2}\) m at \(30\) N, \(15\times10^{-2}\) m at \(45\) N, and \(20\times10^{-2}\) m at \(60\) N.
(a) Force constant of the spring
The force constant \(k\) is the slope (gradient) of the force-extension graph:
\[ k = \frac{\Delta F}{\Delta e} = \frac{60 - 0}{(20 - 0)\times10^{-2}} = \frac{60}{20\times10^{-2}} = \frac{60}{0.20} = 300\ \text{N m}^{-1} \]Any point on the line gives the same value, e.g. \(30 / 0.10 = 300\ \text{N m}^{-1}\). Hence the force constant is 300 N m\(^{-1}\).
(b) Work done in stretching from \(10\times10^{-2}\) m to \(20\times10^{-2}\) m
The work done equals the area under the force-extension graph between the two extensions. From the graph, at \(e_1 = 10\times10^{-2}\) m the force is \(F_1 = 30\) N, and at \(e_2 = 20\times10^{-2}\) m the force is \(F_2 = 60\) N. This shaded region is a trapezium:
\[ W = \tfrac{1}{2}(F_1 + F_2)(e_2 - e_1) = \tfrac{1}{2}(30 + 60)\,(20 - 10)\times10^{-2} \]\[ W = \tfrac{1}{2}(90)(10\times10^{-2}) = \tfrac{1}{2}(90)(0.10) = 4.5\ \text{J} \]Equivalently, using \(W = \tfrac{1}{2}k(e_2^{2} - e_1^{2})\):
\[ W = \tfrac{1}{2}(300)\big[(0.20)^{2} - (0.10)^{2}\big] = 150\,(0.04 - 0.01) = 150 \times 0.03 = 4.5\ \text{J} \]The work done in stretching the spring is 4.5 J.
Pregunta 64 Informe
(a) Distinguish between the forces of adhesion and cohension
(b) Give one example each of the forces of adhesion and cohesion.
(a) Adhesion versus cohesion
Adhesive force is the force of attraction between the molecules of two different substances (unlike molecules).
Cohesive force is the force of attraction between the molecules of the same substance (like molecules).
(b) One example each
- Adhesion: water wetting and sticking to the surface of a clean glass (or ink sticking to paper; water clinging to glass walls).
- Cohesion: mercury forming rounded droplets, or water molecules holding together to form a drop (or mercury not wetting glass).
Detalles de la respuesta
(a) Adhesion versus cohesion
Adhesive force is the force of attraction between the molecules of two different substances (unlike molecules).
Cohesive force is the force of attraction between the molecules of the same substance (like molecules).
(b) One example each
- Adhesion: water wetting and sticking to the surface of a clean glass (or ink sticking to paper; water clinging to glass walls).
- Cohesion: mercury forming rounded droplets, or water molecules holding together to form a drop (or mercury not wetting glass).
Pregunta 65 Informe
(a) State the conditions for the equilibrium of a rigid body acted upon by parallel forces.
(b)(i) Describe an experiment to determine the mass of a metre rule using the principle of moments.
(ii) State two precautions necessary to obtain accurate results in the experiment described in (b)(i) above.
(c) A bullet of mass 120 g is fired horizontally into a fixed wooden block with a speed of 20 ms\(^{-1}\). If the bullet is brought to rest in the block in 0.1s by a constant resistance, calculate the (i) magnitude of the resistance; (ii) distance moved by the bullet in the wood.
(a) Conditions for equilibrium under parallel forces:
- The sum of the forces in one direction equals the sum of the forces in the opposite direction (net force = 0).
- The sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point (net moment = 0).
(b)(i) Experiment to find the mass of a metre rule: Suspend the metre rule from a knife-edge and find its centre of gravity \(G\) (the balance point with no load). Hang a known mass \(m\) at a distance \(d_1\) on one side of a chosen pivot, and adjust the position of the pivot until the rule balances horizontally. Measure the distance \(d_2\) from the pivot to \(G\) (through which the whole weight \(W = Mg\) of the rule acts). Taking moments about the pivot:
\[ m g \times d_1 = M g \times d_2 \Rightarrow M = \frac{m \, d_1}{d_2} \]which gives the mass \(M\) of the rule.
(ii) Two precautions:
- Ensure the rule is horizontal (balanced) before taking readings.
- Avoid parallax error when reading the ruler; ensure the knife-edge is sharp and the mass is firmly fixed.
(c) Bullet mass \(m = 120\ \text{g} = 0.12\ \text{kg}\), \(u = 20\ \text{ms}^{-1}\), \(v = 0\), \(t = 0.1\ \text{s}\).
(i) Resistance (retarding force):
\[ F = \frac{m(u - v)}{t} = \frac{0.12 \times (20 - 0)}{0.1} = \frac{2.4}{0.1} = 24\ \text{N} \](ii) Distance moved in the wood (average velocity method):
\[ s = \left(\frac{u + v}{2}\right) t = \left(\frac{20 + 0}{2}\right) \times 0.1 = 10 \times 0.1 = 1.0\ \text{m} \]The resistance is \(24\ \text{N}\) and the bullet travels \(1.0\ \text{m}\) into the block.
Detalles de la respuesta
(a) Conditions for equilibrium under parallel forces:
- The sum of the forces in one direction equals the sum of the forces in the opposite direction (net force = 0).
- The sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point (net moment = 0).
(b)(i) Experiment to find the mass of a metre rule: Suspend the metre rule from a knife-edge and find its centre of gravity \(G\) (the balance point with no load). Hang a known mass \(m\) at a distance \(d_1\) on one side of a chosen pivot, and adjust the position of the pivot until the rule balances horizontally. Measure the distance \(d_2\) from the pivot to \(G\) (through which the whole weight \(W = Mg\) of the rule acts). Taking moments about the pivot:
\[ m g \times d_1 = M g \times d_2 \Rightarrow M = \frac{m \, d_1}{d_2} \]which gives the mass \(M\) of the rule.
(ii) Two precautions:
- Ensure the rule is horizontal (balanced) before taking readings.
- Avoid parallax error when reading the ruler; ensure the knife-edge is sharp and the mass is firmly fixed.
(c) Bullet mass \(m = 120\ \text{g} = 0.12\ \text{kg}\), \(u = 20\ \text{ms}^{-1}\), \(v = 0\), \(t = 0.1\ \text{s}\).
(i) Resistance (retarding force):
\[ F = \frac{m(u - v)}{t} = \frac{0.12 \times (20 - 0)}{0.1} = \frac{2.4}{0.1} = 24\ \text{N} \](ii) Distance moved in the wood (average velocity method):
\[ s = \left(\frac{u + v}{2}\right) t = \left(\frac{20 + 0}{2}\right) \times 0.1 = 10 \times 0.1 = 1.0\ \text{m} \]The resistance is \(24\ \text{N}\) and the bullet travels \(1.0\ \text{m}\) into the block.
