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**Question 1**
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Which of the following statements about solid friction are correct? It i. is a force ii. occurs between the surfaces of two bodies in contact iii. depends on the area in contact

**Question 2**
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When an object is placed at the centre of curvature of a concave mirror, its image is formed at

**Answer Details**

When an object is placed at the centre of curvature of a concave mirror, its image is formed at the centre of curvature. The centre of curvature is a point on the principal axis of the mirror, located at a distance equal to the radius of curvature from the mirror's vertex. When light rays from the object fall on the concave mirror, they reflect and converge at the centre of curvature. This convergence of light rays forms a real, inverted image of the object at the centre of curvature. Since the image is formed by the actual convergence of light rays, it is a real image. In summary, when an object is placed at the centre of curvature of a concave mirror, its image is formed at the same location, which is the centre of curvature of the mirror.

**Question 3**
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A body moving with an initial velocity U accelerates until it attains a velocity of V within a time t. The distance, s covered by the body is given by the expressions

**Answer Details**

The equation that relates initial velocity, final velocity, acceleration, time and distance is given by s = ut + 0.5at^2 + \(\frac{1}{2}\) at^2. We are given that the body is moving with an initial velocity U and attains a final velocity V within time t. Hence, the acceleration of the body can be calculated using the equation: a = (V - U) / t. Now, substituting the value of acceleration in the above equation, we get: s = Ut + \(\frac{1}{2}\)(V - U)t = \(\frac{V+U}{2}\)t Therefore, the expression for the distance, s covered by the body is s = (\(\frac{V+U}{2}\))t. Hence, option (C) is the correct answer.

**Question 4**
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Which of the following observations is not an effect of surface tension?

**Answer Details**

The observation that is not an effect of surface tension is "water flowing out more easily than engine oil from a container." Surface tension is the cohesive force that exists between molecules at the surface of a liquid, which causes the surface to behave like an elastic film. This property of liquids has several effects, such as the formation of droplets, the spherical shape of mercury droplets, and the ability of small insects to walk on the surface of water. However, the flow rate of a liquid out of a container is not directly related to surface tension. It is primarily determined by the viscosity of the liquid, which is a measure of its resistance to flow. Engine oil is more viscous than water, so it flows more slowly out of a container. This difference in viscosity is why engine oil is thicker and more sluggish than water. In summary, the rate of flow of a liquid out of a container is determined by its viscosity and not surface tension, which only affects the surface properties of the liquid.

**Question 5**
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The distance between two points P and Q, along a wave is 0.05m. If the wave length of the wave is 0.10m, determine the phase angle between P and Q in radians

**Answer Details**

The phase angle between two points on a wave is given by the fraction of the wavelength between the points, measured in radians. In this case, the distance between points P and Q is half the wavelength (0.05m is half of 0.10m). Therefore, the phase angle between P and Q is half of the complete wave cycle, which is equal to π radians. So, the answer is: \(\pi\)

**Question 6**
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The pressure of a fixed mass of an ideal gas at 27°C is 3 pa. The gas is heated at a constant volume until its pressure is 5 pa. Determine the new temperature of the gas.

**Question 7**
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Which of the following statements distinguishes thermal conduction for convection? i. Conduction requires a material medium while convection does not ii. In convection, there is actual motion of hot material, while in conduction, molecules molecules vibrates faster about their mean positions iii. Conduction takes place in solids while convection takes place in fluids.

**Answer Details**

Statement ii and iii distinguish thermal conduction from convection. Thermal conduction refers to the transfer of heat energy through a medium without any actual motion of the medium itself. In conduction, heat is transferred by the transfer of kinetic energy from one molecule to another through collisions. As a result, in conduction, molecules vibrate faster about their mean positions. On the other hand, convection is the transfer of heat energy by the actual movement of a fluid. In convection, hotter and less dense fluids rise while cooler and denser fluids sink, creating a circular motion that transfers heat energy from one place to another. Statement i is incorrect because both conduction and convection require a medium through which heat can be transferred. Statement iii is also incorrect because both thermal conduction and convection can occur in both solids and fluids. Therefore, the correct answer is ii and iii only.

**Question 8**
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Which of the following phenomena is not a direct consequence of rectilinear propagation of light?

**Answer Details**

The phenomenon that is not a direct consequence of rectilinear propagation of light is diffraction of light. Rectilinear propagation of light means that light travels in a straight line in a uniform medium. Lunar and solar eclipses, images of objects in a pinhole camera, and shadows of opaque objects can all be explained by the principle of rectilinear propagation of light. However, diffraction of light is a bending of light waves around obstacles or through narrow slits, and it cannot be explained by the principle of rectilinear propagation of light. Diffraction is a result of the wave nature of light and occurs when light waves encounter obstacles that are comparable in size to the wavelength of light.

**Question 9**
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A plane inclined at 30^{o} to the horizontal has an efficiency of 50%. Calculate the force parallel to the plane required to push a load of 120N uniformly upn the plane

**Answer Details**

When an object is on an inclined plane, its weight is resolved into two components: one perpendicular to the plane, and the other parallel to the plane. The perpendicular component is counteracted by the normal force of the plane, while the parallel component is responsible for the object's motion along the plane. Since the plane has an efficiency of 50%, it means that only half of the force parallel to the plane is used to move the object up the plane. The other half is lost due to friction and other factors. Therefore, to calculate the required force parallel to the plane, we need to divide the weight of the load by the efficiency: force = (load weight / efficiency) * sin(theta) where theta is the angle of inclination of the plane. Substituting the given values, we get: force = (120 / 0.5) * sin(30) force = 240N * 0.5 force = 120N Therefore, the force required to push the load uniformly up the plane is 120N, which corresponds to.

**Question 10**
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An object of mass 2 kg moves with a uniform speed of 10ms^{-1} for 5s along an straight path. Determine the magnitude of its acceleration

**Answer Details**

Since the object is moving with a constant velocity, its acceleration is zero. This is because acceleration is the rate of change of velocity over time, and if the velocity is constant, there is no change and hence, no acceleration. Therefore, the answer is (a) 0 ms^{-2}.

**Question 11**
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The number of protons in an element increased by one after a radioactive decay. The element must have decay by emitting

**Answer Details**

When the number of protons in an element increases by one, it means that a proton has been added to the nucleus of the atom. This can only happen through the emission of a beta particle, which is essentially an electron that is emitted from the nucleus. During beta decay, a neutron in the nucleus of the atom is converted into a proton and an electron. The proton remains in the nucleus, increasing the atomic number by one, while the electron is emitted from the nucleus as a beta particle. Therefore, if the number of protons in an element increases by one, it must have undergone beta decay by emitting a beta particle. Alpha decay involves the emission of an alpha particle, which is made up of two protons and two neutrons. Gamma decay, on the other hand, involves the emission of a gamma ray, which is a high-energy photon. Neutron emission occurs when an unstable nucleus has too many neutrons, but this does not change the atomic number of the element.

**Question 12**
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An object is placed 10cm in front of a plane mirror. If it is moved 8cm away father away from the mirror, determine the distance of the final image from the mirror

**Answer Details**

When an object is placed in front of a plane mirror, its image is formed behind the mirror at the same distance as the object is from the mirror. In this case, the object is placed at a distance of 10 cm from the mirror. Therefore, the image will also be formed at a distance of 10 cm behind the mirror. When the object is moved 8 cm farther away from the mirror, its new distance from the mirror will be 18 cm (10 cm + 8 cm). Since the image distance from the mirror is always equal to the object distance from the mirror, the distance of the final image from the mirror will also be 18 cm. Therefore, the correct answer is: 18cm

**Question 13**
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Which of the following components is used for storing electric charges?

**Answer Details**

A capacitor is the component used for storing electric charges. A capacitor consists of two conductors separated by an insulator, called a dielectric. When a potential difference is applied across the conductors, electrons accumulate on one conductor and are depleted from the other, resulting in an electric field between the conductors. The insulator prevents the electrons from flowing between the conductors, so the charge is stored on the conductors, effectively storing electric charges. The ability of a capacitor to store charge is measured in farads, and capacitors are commonly used in electronic circuits for a variety of applications, including filtering, timing, and power storage.

**Question 14**
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In which of the following piece of apparatus is the radius of curvature equal to twice the focal length?

**Question 15**
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A body of mass 200g and specific heat capacity 0.4Jg^{-1}k^{-1} cools from 37^{o}C to 31^{o}C. Calculate the quantity of the heat released by the body.

**Answer Details**

The quantity of heat released by the body can be calculated using the formula: Q = mcΔT where Q is the quantity of heat, m is the mass of the body, c is the specific heat capacity, and ΔT is the change in temperature. Substituting the given values: m = 200g = 0.2kg c = 0.4Jg^-1k^-1 ΔT = (31 - 37)°C = -6°C Q = (0.2kg) x (0.4Jg^-1k^-1) x (-6°C) = -0.48J The negative sign indicates that the body released heat to the surroundings, which is the expected outcome since the body cooled down. Thus, the correct answer is 0.48J. However, none of the given options match this value exactly. The closest option is 480J, but this is off by a factor of 1000.

**Question 16**
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Which of the following statements is correct about resonance? Resonance occurs when a body

**Question 17**
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A sounding tuning fork is brought near the open end of a pipe containing air and the loudness of the sound is observed to increase. This observation is due to

**Answer Details**

The observed increase in the loudness of the sound when a tuning fork is brought near the open end of a pipe containing air is due to resonance. Resonance occurs when an object is forced to vibrate at its natural frequency by an external force. In this case, the tuning fork produces sound waves at a specific frequency, which matches the natural frequency of the air column in the pipe. As a result, the air column in the pipe begins to vibrate with greater amplitude, which in turn increases the loudness of the sound. This phenomenon is similar to how pushing a child on a swing at the right time will cause them to swing higher and higher. In both cases, the external force is applied at just the right frequency to match the natural frequency of the object, resulting in increased amplitude. Therefore, the correct option is "resonance."

**Question 18**
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In a nuclear reactor, chain reactions result from the release of

**Answer Details**

In a nuclear reactor, chain reactions result from the release of neutrons. A nuclear chain reaction occurs when a neutron collides with a nucleus of a fissile material, such as uranium-235 or plutonium-239, which then splits into two smaller nuclei, releasing energy in the form of heat and more neutrons. These newly released neutrons can then collide with other fissile nuclei, causing them to split and release more neutrons, which continue the chain reaction. This chain reaction is carefully controlled in a nuclear reactor to produce a steady supply of heat that is used to generate electricity.

**Question 19**
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There is always an uncertainty involved in any attempt to measure the position and momentum of an electron simultaneously. This statement is known as the

**Answer Details**

The statement "There is always an uncertainty involved in any attempt to measure the position and momentum of an electron simultaneously" is known as the Heisenberg uncertainty principle. It states that it is impossible to simultaneously determine the precise position and momentum of a subatomic particle such as an electron. The more precisely we know the position of an electron, the less precisely we can know its momentum, and vice versa. This principle is a fundamental concept in quantum mechanics and has important implications for our understanding of the behavior of particles at the subatomic level.

**Question 20**
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A car of mass 800kg moves from rest on a horizontal track and travels 60m in 20s with uniform acceleration. Assuming there were no frictional forces, calculate the accelerating force

**Question 21**
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The ice and steam point on a mercury-in-glass thermometer are 10cm and 30cm respectively. Calculate the temperature in decree Celsius when the mercury meniscus is the 14cm mark

**Answer Details**

We can use the principle of the thermometer, which states that the volume of the liquid (in this case, mercury) in the bulb and stem of the thermometer changes with temperature, and this change in volume is linearly related to the temperature. Therefore, we can set up a proportion: change in volume of mercury / total length of thermometer stem = change in temperature / temperature interval between ice and steam points Let x be the length of the mercury column when the temperature is at the desired point. Then the change in volume of mercury is 14 - 10 = 4 cm. The total length of the stem is 30 - 10 = 20 cm. The temperature interval between ice and steam points is 100^{o}C. Substituting these values into the proportion, we get: 4 cm / 20 cm = change in temperature / 100^{o}C Solving for the change in temperature, we get: change in temperature = (4 cm / 20 cm) * 100^{o}C = 20^{o}C To get the actual temperature at the 14 cm mark, we add the change in temperature to the ice point temperature (which is 0^{o}C): temperature at 14 cm mark = 0^{o}C + 20^{o}C = 20^{o}C Therefore, the answer is 20^{o}C.

**Question 22**
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A rectangular glass prism of thickness d and absolute refractive index n is placed on a point object which is viewed vertically downward from above the prism. Which of the following expressions correctly defines the apparent upward displacement of the object?

**Question 23**
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Calculate the effective resistance between P and Q in the diagram above

**Question 24**
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Which of the following wave is electromagnetic?

**Answer Details**

Electromagnetic waves are waves that are capable of propagating through a vacuum or through different media. These waves are made up of changing electric and magnetic fields that are perpendicular to each other and to the direction of the wave's propagation. Sound waves, water waves, and tidal waves are all mechanical waves, meaning they require a medium to propagate through. X-rays, on the other hand, are electromagnetic waves, which means they do not require a medium to propagate through and can travel through a vacuum. Therefore, the correct answer is x-rays.

**Question 25**
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The correct sequence of energy transformation in the operation of an x-ray tube is i. X-rays ii. Kinetic energy of thermo electrons iii. Potential energy of the target atoms iv. Heat energy of the emitted electrons

**Question 26**
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a body moving at a constant speed accelerates when it is in

**Question 27**
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Mechanical energy can be either

**Answer Details**

Mechanical energy is the energy possessed by an object due to its motion or position. It can be either potential energy or kinetic energy. Potential energy is the energy an object possesses due to its position, shape, or state. Kinetic energy, on the other hand, is the energy an object possesses due to its motion. Therefore, the correct answer is "potential or kinetic."

**Question 28**
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A dry plastic comb used in combing hair was found to attract pieces of paper and dust. The most probable explanation for this phenomenon is that the comb has been given

**Answer Details**

The most probable explanation for the phenomenon of a dry plastic comb attracting pieces of paper and dust is that the comb has been electrically charged by friction. When the comb is rubbed against hair, electrons are transferred from the hair to the comb, leaving the comb with a negative charge and the hair with a positive charge. The negative charge on the comb can then attract positively charged pieces of paper and dust. This process is called charging by friction or triboelectric charging. Therefore, "electric charges by friction" is the correct answer.

**Question 29**
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A swinging pendulum between the rest position and its maximum displacement possesses

**Answer Details**

A swinging pendulum between the rest position and its maximum displacement possesses both kinetic and potential energy. As the pendulum moves away from its rest position, it gains potential energy due to the increased height above the rest position. As the pendulum swings back towards the rest position, it loses potential energy and gains kinetic energy due to its increased speed. At the rest position, the pendulum has its maximum kinetic energy and minimum potential energy, and at the maximum displacement, it has its maximum potential energy and minimum kinetic energy. Thus, the pendulum continuously converts potential energy to kinetic energy and back again, and possesses both types of energy at any point during its motion.

**Question 30**
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A body accelerates uniformly from rest at 2ms^{-2}. Calculate the magnitude of its velocity after travelling 9m

**Answer Details**

To solve this problem, we can use the kinematic equation: v^{2} = u^{2} + 2as Where: v = final velocity (what we want to find) u = initial velocity (in this case, 0 since the body starts from rest) a = acceleration (given as 2 ms^{-2}) s = distance travelled (given as 9m) Substituting the given values, we get: v^{2} = 0^{2} + 2 x 2 ms^{-2} x 9m v^{2} = 36 ms^{-1} v = √(36) ms^{-1} Therefore, the magnitude of the velocity of the body after travelling 9m with a uniform acceleration of 2ms^{-2} is 6.0 ms^{-1}.

**Question 31**
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Which of the following operations does not represent an action of a force field?

**Answer Details**

The operation that does not represent an action of a force field is the "pushing of a wheel-barrow on a level ground". A force field is a region where a force acts on an object, and the object experiences a force because of the interaction with the field. In the case of the pushing of a wheel-barrow, the force is not a result of a field but is applied by the person pushing the wheelbarrow. Therefore, this operation does not represent an action of a force field.

**Question 32**
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A relative density bottle of volume 50cm^{3} is completely filled with a liquid at 30^{o}C. It is then heated to 80^{o}C such that 0.75cm^{3} of the liquid is expelled. Calculate the apparent cubic expansivity of the liquid.

**Question 33**
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The diagram above illustrates three forces acting on an object at point O. If the object is in equilibrium, determine the magnitude of the force P.

**Question 34**
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Which of the following factors can affect the speed of sound in air? i. The temperature of the surrounding ii. The direction of the wind iii. The pitch of the sound.

**Question 35**
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Which of the following surfaces will radiate heat energy best?

**Answer Details**

A black surface will radiate heat energy best. This is because black surfaces are good absorbers of all wavelengths of light, including infrared radiation, which is the type of radiation associated with heat energy. As a result, they also emit more radiation at these wavelengths, making them better at radiating heat energy compared to surfaces that reflect or transmit more light, such as white, yellow, or red surfaces.

**Question 36**
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According to the kinetic theory of gasses, which of the following property of a gas can be affected by the collision of the gas molecule with the walls of the container?

**Answer Details**

According to the kinetic theory of gases, the pressure of a gas can be affected by the collision of gas molecules with the walls of the container. As the gas molecules move randomly, they collide with the walls of the container and exert a force on it. This force per unit area is defined as the pressure of the gas. The more frequent and intense the collisions, the higher the pressure. Therefore, the pressure of a gas can be increased or decreased by changing the number of collisions with the walls of the container. The other options listed (temperature, energy, viscosity) are also properties of gases, but they are not directly affected by collisions with the walls of the container.

**Question 37**
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A block of mass 4.0kg causes a spiral spring to extend by 0.16m from its unstretched position. The block is removed and another body of mass 0.50kg is hung from the same spiral spring. If the spring is then stretched and released, what is the angular frequency of the subsequent motion? [g = 10 ms ^{-2}]

**Question 38**
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The team rectilinear acceleration means the rate of increase of

**Answer Details**

The term "rectilinear acceleration" refers to the rate of change or increase in velocity along a straight-line path in a unit time. It is also known as linear acceleration or simply acceleration. Therefore, the correct option is: velocity along a straight-line path in a unit time.

**Question 39**
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Which of the following electromagnetic wave can be detected by its heating effect?

**Answer Details**

Infrared radiation can be detected by its heating effect. Infrared radiation is a type of electromagnetic radiation that has longer wavelengths than visible light. When infrared radiation falls on an object, the energy is absorbed by the object, causing the object's temperature to increase. This effect is commonly used in devices such as infrared heaters and thermal imaging cameras, which use infrared radiation to detect the heat signature of objects. Therefore, option D (infrared radiation) is the correct answer to the question.

**Question 40**
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An external force of magnitude 100N acts on a particle of mass 0.15kg for 0.03s. Calculate the change in the speed of the particle

**Answer Details**

The change in the speed of the particle can be calculated using the formula: Δv = FΔt/m Where Δv is the change in velocity (speed), F is the external force applied, Δt is the time for which the force is applied, and m is the mass of the particle. Substituting the given values, we get: Δv = (100N) x (0.03s) / 0.15kg Δv = 20ms^{-1} Therefore, the change in the speed of the particle is 20ms^{-1}. This means that the speed of the particle increased by 20 meters per second during the time when the external force was applied.

**Question 41**
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Which of the following physical quantities is correctly paired with it's corresponding S.I unit?

**Question 42**
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Five 80-W and three 100W are run for 8 hours. If the cost of energy is N5.00 per unit, calculate the cost of running the lamp. [1 unit = 1 kWh]

**Answer Details**

The total energy consumed by the lamps can be calculated by first finding the total power rating of the lamps, and then multiplying it by the time they were used. Total power = (5 x 80W) + (3 x 100W) = 400W + 300W = 700W Total energy = Power x Time = 700W x 8 hours = 5600 Wh = 5.6 kWh Since 1 unit = 1 kWh, the energy consumed is 5.6 units. The cost of running the lamps can then be calculated by multiplying the energy consumed by the cost per unit of energy. Cost = Energy consumed x Cost per unit = 5.6 units x N5.00 per unit = N28.00 Therefore, the cost of running the lamps is N28.00. Answer is the correct answer.

**Question 43**
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A liquid of volume 2.00 m^{3} and density 1.00 x 10^{3} is mixed with 3.00 m^{3} of another liquid of density 8.00 x 10^{3}kg m^{-3}. Calculate the density of the mixture [Assuming there is no chemical reaction]

**Question 44**
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A bulb marked 240V, 40W is used for 30 minutes. Calculate the heat generated

**Answer Details**

The formula for calculating electrical energy is given by: E = P x t Where E is the energy in joules, P is the power in watts, and t is the time in seconds. Firstly, we need to convert the time of 30 minutes to seconds. 30 minutes = 30 x 60 seconds = 1800 seconds The power of the bulb is given as 40W, and the voltage is given as 240V. We can use these values to calculate the current (I) flowing through the bulb: Power (P) = Voltage (V) x Current (I) Current (I) = Power (P) / Voltage (V) Current (I) = 40 / 240 = 0.1667 A (to 4 decimal places) Now we can use the formula for energy to calculate the heat generated: E = P x t E = 40 x 1800 E = 72000 J Therefore, the answer is 72000J. So, the correct option is 4) 72000J.

**Question 45**
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A mass of mass m, experiences a viscous drag, F and an upthrust, U as he descends towards the ground at a steady velocity, Using a parachute. If the acceleration of free fall is g, which of the following expressions is correct?

**Answer Details**

When an object is descending at a steady velocity, the forces acting on it must be balanced. Therefore, the net force on the object must be zero. In this case, the forces acting on the mass are the viscous drag force, F, the upthrust force, U, and the force due to gravity, mg. Using Newton's second law, we know that the net force on an object is equal to its mass times its acceleration. Since the object is descending at a steady velocity, its acceleration is zero, so the net force on the object must also be zero. Therefore, we can write the following equation: U + F - mg = 0 This equation shows that the upthrust force and the viscous drag force must balance the force due to gravity in order for the object to descend at a steady velocity with a parachute. So, the correct expression is: U + F - mg = 0.

**Question 46**
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Which of the following statements about sound wave is not correct? Sound waves can be

**Answer Details**

The statement that sound waves can be polarized is not correct. Polarization refers to the orientation of the electric field component of a transverse wave. However, sound waves are longitudinal waves, which means that they oscillate in the same direction as the wave propagation. Therefore, sound waves do not have an electric field component and cannot be polarized. On the other hand, sound waves can be reflected, refracted, and diffracted. Reflection occurs when a sound wave bounces off a surface, such as an echo in a room. Refraction occurs when a sound wave bends as it passes through a medium with a different density, such as when sound waves pass through air with different temperatures. Diffraction occurs when a sound wave bends around obstacles in its path, such as when sound waves from a speaker spread out in all directions.

**Question 47**
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If a gas is excited by high voltage to produce a discharge and the light is examined in a spectrometer

**Answer Details**

When a gas is excited by high voltage to produce a discharge and the light is examined in a spectrometer, an emission spectrum is observed. This is because the excited gas atoms emit energy in the form of light of specific wavelengths as they return to their ground state. These emitted wavelengths are characteristic of the element or compound being examined and appear as bright lines in the spectrum. Therefore, the emission spectrum can be used to identify the elements present in the gas being examined.

**Question 48**
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A cube made of metal of linear expansivity \(\alpha\) is heated through a temperature \(\theta\). If the initial volume of the cube is V_{o}, the correct expression for the increase in volume of the cube is

**Question 49**
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Copper of thickness d is plated on the cathode of a copper voltameter. If the total surface area of the cathode is 60 cm\(^2\) and a steady current of 5.0 A is maintained in the voltameter for 1 hour. calculate the value of d. [density of copper = 8.9 x 10\(^3\)kg m\(^{-3}\) electro chemical equivalent of copper = 3.3 x 10\(^{-7}\) kg C\(^{-1}\)

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**Question 50**
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(a) Define the boiling point of a liquid.

(b) With the aid of a sketch diagram, describe an experiment to determine the boiling point of a small quantity of a Iiquid

(c) A piece of copper of mass 300 g at a temperature of 950°C is quickly transferred into a vessel of negligible thermal capacity containing 250 g of water at 25°C. If the final steady temperature of the mixture is 100°C, calculate the mass of water that will boil away. Especific heat capacity of copper = 4.0 x 10\(^2\) J kg\(^{-1}\)K\(^{-1}\) specific heat capacity of water = 4.2 x 10\(^{3}\) J kg\(^{-1}\)K\(^{-1}\) specific latent heat of vaporization of steam = 2.26 x 10\(^6\)J kg\(^{-1}\)

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**Question 51**
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(a)(i) What is a wave motion?

(ii) State two differences between a radio wave and a sound wave.

(b)(i) Given that you are provided with a tuning fork, a burette and other necessary apparatus, describe with the aid of a diagram, an experiment to determine the frequency of a note emitted by a source of sound. [assume the velocity of sound in air is known]

(ii)State two precautions necessary to obtain accurate result in the experiment described in (b)(i) above

(c) A pipe closed at one end is 100 cm long. If the air in the pipe is set into vibration and a fundamental note is produced, calculate the frequency of the note. [ velocity of sound in air = 340 ms\(^{-1}\)]

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**Question 52**
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State two effects to show (a) the existence of matter waves;

(b) that radiation behaves like particles.

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**Question 53**
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(a) Explain thermiopic emission

(b) State two applications of electrical conduction through gases.

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**Question 54**
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A wire of length 5.0 m and diameter 2.0 mm extends by 0.25 mm when a force of 50 N was used to stretch it from its end. Calculate the;

(a) stress on the wire;

(b) strain in, the wire. [\(\pi = 3.142\)]

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**Question 55**
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A particle is projected at an angle of 30° to the horizontal with a speed of 250 ms\(^{-1}\). Calculate the;

(a) total time of flight of the particle;

(b) speed of the particle at its maximum height. [ g = 10 ms\(^{-2}\)]

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**Question 56**
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(a) State the conditions of equilibrium for a number of coplanar parallel forces.

(b) A metre rule is found to balance horizontally at the 48 cm mark. When a body of mass 60 g is suspended at the 6 cm mark, the balance point is found to be at the 30 cm mark. Calculate the;

(i) mass of the metre rule;

(ii) distance of the balance point from the zero end, if the body were moved to the 13 cm mark.

(c) a man pulls up a box of mass 70 kg using an inclined plane of effective length 5 m unto a platform 2.5 m high at a uniform speed. If the frictional force between the box and the plane is 1000 N;

(i) draw a diagram to illustrate all the forces acting on the box while in motion;

(ii) calculate the I. minimum effort applied in pulling up the box; II. velocity ratio of the plane, if it is inclined at 30° to the horizontal; Ill. force ratio of the plane.

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**Question 57**
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A stone projected horizontally from the top of a tower with a speed of 4 ms\(^{-1}\) lands on the level ground at a horizontal distance 25 m from the foot of the tower. Calculate the height of the tower. g = 10 ms\(^{-2}\)]

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**Question 58**
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Define (a) tensile Stress; (b) tensile strain; (c) yield point.

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**Question 59**
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**TEST OF PRACTICAL KNOWLEDGE QUESTION**

You have been provided with an accumulator **E**, a standard resistor **Rx**, two resistance boxes **RB**\(_{1}\) and RB\(_{2}\), two keys K\(_{1}\) and K\(_{2}\) and other necessary apparatus.

- Measure and record the e.m.f of the accumulator.
- Connect a circuit as shown above.
- Set the resistance R, in the resistance box such that R in
**RB**\(_{1}\) = R in RB\(_{2}\) = 1\(\Omega\). - With K\(_{1}\) open and K\(_{2}\) closed, measure and record the potential difference V across the standard resistor Rx. (v) Close K, and K,. Read and record the potential difference V\(_{o}\) across
**Rx**. - Evaluate V\(_{1}^{-1}\)
- Repeat procedure (v) for four other values of R = 2, 3, 4 and 5\(\Omega\) respectively. In each case, ensure that the value of
**R**in**RB**\(_{1}\) is equal to the value of R in**RB**\(_{2}\). - Evaluate V\(_{1}^{-1}\) in each case. Tabulate your readings.
- Plot a graph of V\(_{1}^{-1}\) on the vertical axis against R on the horizontal axis starting both axes from the origin (0,0).
- Determine the slope, s, of the graph and the intercept on the vertical axis.
- Evaluate y = \(\frac{1}{s}\)
- State two precautions taken to ensure accurate results

(b)i. Explain what is meant by the potential difference between two points in an electric circuit

ii. A cell has an e.m.f. of 3 V. When it is connected across a resistor of resistance 4\(\Omega\), a current 0.5A passes through the circuit. Calculate the internal resistance of the cell.

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**Question 60**
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**TEST OF PRACTICAL KNOWLEDGE QUESTION**

You are provided with a retort stand, clamp and boss, a pendulum bob, a piece of thread, and other necessary apparatus. Carry out the fo lowing experiment:

- Set up the apparatus as shown in the diagram above:
- measure and record the distance = 130cm from the centre of the bob to the point of suspension of the pendulum
- displace the pendulum through a small angle and release. Allow the pendulum to oscillate freely;
- determine the time
**t**for 20 complete oscillations; - also, determine the period T of the oscillations
- evaluate T\(^{2}\) and L = -30;
- repeat the procedure for four other values of l = 110, 90, 70, and 50 cm
- in each case, determine t and evaluate T,T\(^{2}\) and L. Tabulate your readings.
- plot of a graph of T\(^{2}\) on the vertical axis against L on the horizontal axis, starting both axes from the origin (0,0)
- determine the slope, s, of the graph. Also determine the intercept, C, of the graph on the T\(^{2}\) axis;
- evaluate: i. k\(_{1}\) = \(\frac{4\pi^{2}}{s_{1}}\),

ii. k\(_{2}\) = \(\frac{c}{8}\) [Take \(\pi\) = \(\frac{22}{7}\)] - state two precautions taken to ensure accurate results.

(b)i. What is meant by the period of oscillation of an oscillating body?

i. Explain the acceleration of free fall due to gravity.

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**Question 61**
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(a) List two factors that can affect the rate of diffusion

(b) State two examples to illustrate the effects of surface tension.

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**Question 62**
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(a)(i) With the aid of a labelled diagram describe the mode of operation of a modern X-ray tube.

(ii)State the energy transformations that take place during the operation of the X-ray tube.

(b) Define, as applied to X-rays, the following terms:

(i) hardness;

(ii) intensity.

(c) State (i) four uses of X-rays;

(ii) one hazard of over-exposure to X-rays in a radiological laboratory.

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**Question 63**
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Define

(a) electrolysis;

(b) electrolyte;

(c) electrode.

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**Question 64**
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(a) With the aid of a simple diagram, explain how a step down transformer works.

(b)(i) State three ways by which energy is lost in a transformer

(ii) Mention how each of the losses in (b)(i) above can be minimized

(c) A 95% efficient transformer is used to operate a lamp rated 60W, 220 V from a 4400 V a.c supply. Calculate the;

(i) ratio of the number of turns in the primary coil to the number of turns in the secondary coil of the transformer

(ii) current taken from the main circuit.

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**Question 65**
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**TEST OF PRACTICAL KNOWLEDGE QUESTION**

Using the above diagram as a guide, carry out the following experiment:

- place the equilateral triangular glass prism on the drawing paper. Trace the outline
**ABC**of the prism. - remove the prism. Draw a line
**NO**such that it makes an angle*i*= 25º with the normal at point**O**on side**AB** - fix two pins
**R\(_{1}\)**and**R\(_{2}\)**vertically on line**N0**. Replace the prism on its outline; - place the reflecting surface of the plane mirror in contact with the face
**AC**of the prism; - looking through the face
**BC**of the prism, fix two other pins at**R\(_{3}\)**and**R\(_{4}\)**such that the pins appear to be in a straight line with the images of the pins at R**\(_{1}\)**and**R\(_{2}\)**; - remove the prism, the mirror, and the pins. Draw a line to join points R
**\(_{4}\)**and**R\(_{3}\)** - produce line
**R\(_{4}\)R\(_{3}\)**to meet line**NO**produced at**T**; - measure and record the angle \(\theta\) at
**T**and**e**at**D**; - repeat the procedure for
**four**other values of*i*= 30°, 35°, 40°, and 45°. In each case, measure and record the corresponding values of \(\theta\) and**e**. Tabulate your readings; - plot a graph of
**e**on the vertical axis and \(\theta\) on the horizontal axis; - evaluate k = s\(^{-1}\)
- state
**two**precautions taken to ensure accurate results. [Attach your traces to your answer booklet]

(b)i. State **four **characteristics of the image of an object formed by a plane mirror.

ii. State two Conditions necessary for total internal reflection to occur in a medium.

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**Question 66**
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State;

(a) the difference between plane polarized light and ordinary light;

(b) two uses of polaroids.

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