WAEC SSCE - Physics - 2002

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To determine the displacement, we need to find the resultant of the two vectors. Using Pythagoras theorem, we can find the magnitude of the resultant vector.

Let's draw a diagram to represent the situation. Let's assume that the starting point is A, the end point is C, and B is the intermediate point.

       6km
         ^
         |
         |
         |
  8km<---C
         |
         |
         |
         A

From the diagram, we can see that the boy has travelled a total distance of 8km + 6km = 14km.

To find the displacement, we can use the Pythagorean theorem:

displacement² = (8km)² + (6km)²

displacement² = 64km² + 36km²

displacement² = 100km²

displacement = 10km

Therefore, the magnitude of the displacement is 10km.

The difference between the magnitude of displacement and distance travelled is:

difference = displacement - distance travelled

difference = 10km - 14km

difference = -4km

Since the displacement is greater than the distance travelled, the boy has some amount of displacement left after travelling the distance. Therefore, the difference is negative, indicating that the magnitude of displacement is 4km less than the distance travelled.

So the answer is -4.0km, but since a negative answer is not one of the options provided, we can assume that the correct answer is 4.0km.

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When capacitors are connected in series, the effective capacitance of the combination is given by: \[\frac{1}{C_{\text{eff}}}=\frac{1}{C_1}+\frac{1}{C_2}+...\frac{1}{C_n}\] where \(C_1\), \(C_2\)...\(C_n\) are the individual capacitances of the capacitors connected in series. In this case, we have three capacitors, each with capacitance 18\(\mu F\), connected in series. So we have: \[\frac{1}{C_{\text{eff}}}=\frac{1}{18\mu F}+\frac{1}{18\mu F}+\frac{1}{18\mu F}=\frac{3}{18\mu F}\] Simplifying the right-hand side, we get: \[\frac{1}{C_{\text{eff}}}=\frac{1}{6\mu F}\] Taking the reciprocal of both sides, we get: \[C_{\text{eff}}=6\mu F\] Therefore, the effective capacitance of the three capacitors in series is 6\(\mu F\). Hence, the answer is: 6.00\(\mu F\)

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A freely-suspended magnet will come to rest with its axis pointing approximately north-south. This is because the magnet aligns itself with the Earth's magnetic field, which runs approximately north-south at most locations on the planet. As the magnet swings, it experiences a torque due to the magnetic field, which causes it to align itself with the field and come to rest with its axis pointing in the direction of the field.

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The velocity of a wave is given by the product of its frequency and wavelength, i.e., velocity = frequency x wavelength Rearranging this equation, we get: frequency = velocity / wavelength Substituting the given values, we get: frequency = (3 x 10^8 m/s) / (150 m) frequency = 2 x 10^6 Hz Therefore, the frequency of the radio wave is 2.0 x 10^6 Hz. Answer: Option D.

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Local actions in a simple electric cell are caused by impurities on the surface of the zinc plate. When impurities on the surface of the zinc plate react with the acid, they form a small cell and cause the zinc to dissolve locally. To prevent local actions, the surface of the zinc plate is amalgamated (i.e. coated with mercury), which provides a uniform surface for the reaction with the acid. This prevents the formation of small cells and ensures that the current flows evenly through the cell. Therefore, the correct option is "amalgamating the surface of the zinc plate".

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The time taken by the pulse of sound to travel from the ship to the sea bed and back to the ship is 0.2 seconds. This time includes the time taken by the pulse to travel from the ship to the sea bed and the time taken by the reflected pulse to travel back from the sea bed to the ship. Let's assume that the depth of the sea is 'd'. So, the total distance travelled by the sound is twice the depth of the sea or 2d. From the formula, distance = speed × time, we can write: 2d = speed of sound × 0.2 Substituting the value of speed of sound in sea water as 1560ms^-1, we get: 2d = 1560 × 0.2 2d = 312 Therefore, the depth of the sea is 312/2 = 156 meters. Hence, the correct option is: - 156.0m

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Increasing the cross-sectional area of the string will not cause an increase in the frequency of a vibrating string. This is because the frequency of a vibrating string is determined by its tension, mass per unit length, and length, but not by its cross-sectional area. Increasing the cross-sectional area of the string will only increase its volume and mass, but will not affect its tension or length, which are the factors that determine the frequency of the string. Therefore, this is the correct answer.

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When a radioactive atom emits a beta particle, a neutron in the nucleus is converted into a proton and an electron. The electron is emitted as a beta particle, while the proton remains in the nucleus. Therefore, the atomic number increases by one, as the nucleus now has one more proton. The mass number, which is the sum of the protons and neutrons in the nucleus, remains the same, since the neutron is converted into a proton, and the mass of a proton is approximately equal to that of a neutron. So, the correct answer is: "remains the same".

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When a spring is compressed or stretched from its natural length, it stores potential energy. The potential energy stored in a spring is given by the formula: U = 1/2 kx^2 where U is the potential energy stored, k is the force constant of the spring and x is the displacement of the spring from its natural length. In this case, the natural length of the spring is 30.0 cm, and it is compressed to a length of 20.0 cm, so its displacement is: x = 30.0 cm - 20.0 cm = 10.0 cm = 0.1 m The force constant of the spring is given as 20 Nm^-1. Therefore, the potential energy stored in the spring is: U = 1/2 (20 Nm^-1) (0.1 m)^2 = 0.1 J Therefore, the energy stored in the spring is 0.1 J.

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The gold leaf electroscope can be used to compare the relative magnitudes of electric charges on two bodies. An electroscope is a device used to detect the presence of an electric charge. When a charged object is brought near the top of the electroscope, the leaves inside the electroscope will either repel or attract each other, indicating the presence and sign of the charge. By using a charged object to charge the electroscope, and then bringing the object whose charge is being tested close to the top of the electroscope, the relative magnitude of the charges on the two objects can be compared. Therefore, the correct option is the "gold leaf electroscope".

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The type of wave produced when the slinky spring is displaced parallel to the table and released is a longitudinal wave. This is because the particles of the slinky move parallel to the direction of propagation of the wave. As the wave travels through the slinky, the coils of the spring compress and stretch alternately, forming areas of high and low pressure. These pressure changes travel along the length of the slinky, causing the wave to propagate. The wavelength of the wave will depend on the frequency of the wave and the speed of propagation, which in turn depend on the properties of the slinky, such as its mass per unit length and tension. The options "transverse", "stationary", and "electromagnetic" do not accurately describe the wave produced by the slinky spring in this scenario.

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In the given wave equation, y = E_o sin(299t - π), E_o represents the amplitude of the wave. The amplitude of a wave refers to the maximum displacement of a particle from its equilibrium position. In other words, it is the distance between the crest or trough of a wave and the equilibrium point. In this equation, the amplitude is given by E_o. Therefore, E_o represents the maximum displacement of the wave from its equilibrium position.

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Increasing the gap between the poles of the magnet will not lead to an increase in the induced e.m.f. in a coil of wire rotating between the poles of the magnet. This is because the magnetic field is weaker at a greater distance from the magnet, and therefore the rate of change of magnetic flux linking with the coil will be smaller. The induced e.m.f. is directly proportional to the rate of change of magnetic flux, so if the flux linkage decreases, the induced e.m.f. will also decrease. On the other hand, increasing the strength of the magnet, the number of turns in the coil, or the speed of rotation of the coil will all increase the rate of change of magnetic flux and hence increase the induced e.m.f.

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To solve this problem, we need to use the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred from one form to another. When the hot water is mixed with the cold water, heat energy flows from the hot water to the cold water until they reach the same temperature. We can use the equation: Q = mCΔT where Q is the amount of heat energy transferred, m is the mass of the water, C is the specific heat capacity of water, and ΔT is the change in temperature. Let's start by finding the amount of heat energy transferred from the hot water to the cold water: Q₁ = (0.12 kg) * (4186 J/kg°C) * (50°C - T) where T is the final temperature of the mixture. We use 4186 J/kg°C as the specific heat capacity of water. Similarly, the amount of heat energy gained by the cold water is: Q₂ = (0.2 kg) * (4186 J/kg°C) * (T - 10°C) Since energy is conserved, we know that Q₁ = Q₂. Therefore: (0.12 kg) * (4186 J/kg°C) * (50°C - T) = (0.2 kg) * (4186 J/kg°C) * (T - 10°C) Solving for T, we get: T = 25°C Therefore, the temperature of the mixture is 25°C. Option (C) is correct. Note: It is important to keep in mind that this calculation neglects any heat losses to the surroundings, which may affect the actual temperature of the mixture in a real-world scenario.

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The correct answer is: their molecules are always in motion. Solids, liquids and gases are the three main states of matter, and they all share the characteristic that their molecules are always in motion. However, the motion of the molecules varies between the three states. In solids, the molecules are packed tightly together and vibrate around fixed positions. In liquids, the molecules have more freedom of movement and can slide past each other. In gases, the molecules move freely and randomly in all directions. None of the other options are correct. Solids and liquids have a fixed volume, but gases do not. The size of the molecules varies between the three states. The intermolecular forces also vary between the states; solids have the strongest intermolecular forces, followed by liquids and then gases.

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The skin of a 'talking' drum performs vibratory motion when it is struck with a drumstick. This is because the drumstick striking the skin creates a disturbance that travels as a wave through the skin. The skin then vibrates back and forth in a periodic motion, producing sound waves in the air. This vibratory motion is what produces the unique sound of the 'talking' drum.

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When the size of the hole in a pinhole camera is increased, the image formed becomes blurred. This is because a larger hole allows more light to enter the camera and hit different parts of the film or image sensor, resulting in a less focused image. The pinhole camera works by allowing light to pass through a tiny aperture, which then projects an inverted image onto the opposite side of the camera. The smaller the aperture, the sharper the image, as the light is more focused and only travels in straight lines. By increasing the size of the hole, the light waves scatter more, resulting in a less clear image.

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The silver coating on the inside of a vacuum flask reduces heat loss by radiation. Heat can be transferred in three ways: conduction, convection, and radiation. In a vacuum flask, the space between the two walls of the flask creates a vacuum which reduces heat transfer by conduction and convection. However, radiation can still occur. The silver coating on the inside of the flask reflects radiant heat back to the liquid, reducing heat loss by radiation. Therefore, the silver coating on the inside of a vacuum flask reduces heat loss by radiation.

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The phenomenon described in the question is called "beats". Beats occur when two sound waves of nearly the same frequency interfere with each other. The interference causes the sound intensity to periodically increase and decrease, creating a pulsing or beating sound. The frequency of the beats is equal to the difference between the frequencies of the two sound waves.

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The relative density of a substance is defined as the ratio of its density to the density of a reference substance. In this case, the reference substance is water. When the solid is in air, it experiences a weight of 45N. This means that the weight of the displaced air is also 45N. Therefore, the density of the solid is: density of solid = weight of solid / volume of solid Since the volume of the solid is the same in air and in water, we can write: density of solid in air = weight of solid / volume of solid = weight of displaced air / volume of solid When the solid is in water, it experiences a weight of 15N. This means that the weight of the displaced water is 45N - 15N = 30N. Therefore, the density of the solid is: density of solid in water = weight of solid / volume of solid = weight of displaced water / volume of solid Now, the relative density of the solid is defined as the ratio of the density of the solid to the density of water: relative density of solid = density of solid / density of water We can substitute the expressions we obtained for the densities of the solid in air and in water: relative density of solid = (weight of displaced air / volume of solid) / (weight of displaced water / volume of solid) Simplifying this expression, we get: relative density of solid = weight of displaced air / weight of displaced water Substituting the values we obtained for the weights of displaced air and water, we get: relative density of solid = 45N / 30N = 1.5 Therefore, the relative density of the solid is 1.5. Answer: 1.50

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The xylophone is not a wind instrument. It is a percussion instrument that produces sound when wooden bars are struck with mallets. In contrast, the clarinet, saxophone, and trumpet are all wind instruments that produce sound through the vibration of air within the instrument.

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To calculate the depth at which the pressure in the liquid will equal to 9100Nm^-2, we can use the formula: pressure = density * gravity * height where density is the density of the liquid, gravity is the acceleration due to gravity, and height is the depth of the liquid. Rearranging this formula to solve for height, we get: height = pressure / (density * gravity) Substituting the given values, we get: height = 9100 / (2000 * 10) = 0.455m Therefore, the depth at which the pressure in the liquid will equal to 9100Nm^-2 is 0.455m. So, the answer is.

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Neutrons are usually used to cause fission in an atomic reactor. In a nuclear reactor, a neutron is fired at the nucleus of an atom of fuel, usually uranium-235 or plutonium-239. The neutron is absorbed by the nucleus, which becomes unstable and breaks apart into two smaller nuclei, releasing energy and more neutrons. These newly-released neutrons then go on to cause fission in other fuel nuclei, resulting in a chain reaction that releases a large amount of energy in the form of heat. This heat is then used to produce steam, which drives a turbine to generate electricity.

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The force between the molecules of a liquid in contact with that of a solid is adhesive. Adhesive force refers to the attractive force between two different substances, such as the force that causes a liquid to "stick" to a solid surface. The adhesive force is due to intermolecular forces, such as hydrogen bonding, that occur between the molecules of the liquid and the molecules of the solid. This force is responsible for phenomena such as capillary action, in which a liquid will "climb" up a narrow tube, and wetting, in which a liquid will spread out over a surface.

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The gravitational attraction between two objects depends on their masses and the distance between them. The formula for calculating gravitational force is: F = G(m1m2)/r^2 Where F is the force, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them. We are given that the gravitational force between the earth and the particle is 40N, and the mass of the particle is 4kg. The mass of the earth is much larger than the mass of the particle, so we can assume that the distance between them is the radius of the earth. The gravitational field intensity at a point is defined as the force per unit mass experienced by a test particle placed at that point. So, the gravitational field intensity of the earth on the particle can be calculated by dividing the gravitational force by the mass of the particle: g = F/m Substituting the given values, we get: g = 40N/4kg g = 10.0N kg^-1 Therefore, the magnitude of the gravitational field intensity of the earth on the particle is 10.0N kg^-1. This is.

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The critical angle is the angle of incidence where the angle of refraction is 90 degrees, and the refracted ray emerges along the boundary between the two media. It can be calculated using the formula: sin(critical angle) = 1/n where n is the refractive index of the medium relative to air. Therefore, sin(critical angle) = 1/1.8 = 0.5556 Using a scientific calculator or a trigonometric table, we can find that the angle whose sine is 0.5556 is approximately 34 degrees. Thus, the critical angle for the medium is 34^o.

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Power is the rate at which work is done or energy is transferred. It is expressed in watts (W). In this question, we are asked to calculate the power generated by the machine which raised a load of mass 120kg through a height of 2m in 30s. The work done by the machine is given by the formula: work = force x distance In this case, the force is equal to the weight of the load, which is given by: force = mass x acceleration due to gravity force = 120kg x 10m/s² = 1200N The distance the load was raised is 2m. So, the work done by the machine is: work = force x distance = 1200N x 2m = 2400J The time taken to do the work is 30s. Therefore, the power generated by the machine is: power = work / time power = 2400J / 30s = 80W So, the correct answer is 80W.

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To determine the weight of object A, we need to consider the forces acting on it. In this case, there are two forces acting on object A: the tension in the string and the weight of object A. The tension in the string is equal and opposite to the weight of the hanging object B. We know that the weight of object B is 17 N, so the tension in the string is also 17 N. Since object A is in equilibrium, the net force acting on it is zero. Therefore, the weight of object A must be equal and opposite to the tension in the string, which is also 17 N. Therefore, the magnitude of the weight of object A is 17 N. is the correct answer.

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The time taken for an object to fall freely from a height h can be calculated using the formula: t = sqrt(2h/g) Where t is the time taken, h is the height and g is the acceleration due to gravity. Substituting the values given, we get: t = sqrt(2 x 25 / 10) = sqrt(5) = 2.24s Therefore, the time it takes to fall to the ground is 2.24s. The correct option is (d).

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The expression that gives the magnitude of the force required to make an object of mass, m move with speed, v in a circular of radius r is given by the formula: \(\frac{mv^2}{r}\). This formula is known as the centripetal force formula. It states that the force required to keep an object moving in a circular path is directly proportional to the mass of the object, the square of its velocity and inversely proportional to the radius of the circular path. So, if we increase the mass of the object, the force required to keep it moving in a circular path will also increase. If we increase the velocity of the object, the force required will increase by a factor equal to the square of the velocity. Finally, if we increase the radius of the circular path, the force required will decrease.

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To improve the efficiency of the pulley system, the action required is to reduce the mass of the pulley. This is because the efficiency of a pulley system is determined by the mechanical advantage, which is the ratio of output force to input force. The output force is the weight of the load being lifted, while the input force is the force applied to the string to lift the load. When the mass of the pulley is reduced, the input force required to lift the load is also reduced, resulting in a higher mechanical advantage and hence, a more efficient pulley system. Increasing the friction force between the string and the pulley, increasing the mass per unit length of the string or increasing the mass of the pulley will have the opposite effect of reducing the mechanical advantage and therefore reducing the efficiency of the pulley system.

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The acceleration of an object is given by the formula: a = (v - u) / t where, a = acceleration v = final velocity u = initial velocity t = time Here, the car starts from rest, which means its initial velocity (u) is zero. The car covers a distance of 80m in a time of 10s. We can use the formula of distance to find the final velocity of the car. s = ut + (1/2)at^2 where, s = distance u = initial velocity t = time a = acceleration As the car starts from rest, its initial velocity is zero, so we can simplify the equation to: s = (1/2)at^2 Rearranging the formula to get acceleration (a), we have: a = 2s / t^2 Substituting the given values, we get: a = 2 x 80m / (10s)^2 = 1.6ms^-2 Therefore, the magnitude of the car's acceleration is 1.6ms^-2. The answer is.

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Boron rods are used to control the rate of neutron production in a nuclear reactor. Boron is a good neutron absorber and it is able to absorb neutrons without itself undergoing fission, so it is used to control the rate of fission in the reactor. By inserting or removing the boron rods from the reactor core, the amount of neutrons available to sustain the fission chain reaction can be controlled, and the reactor's power output can be adjusted accordingly.