WAEC SSCE - Physics - 1989

The electric force between two point charges each of the magnitude, q at a distance of r apart in air of permittivity is:

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The refractive index of a given transparent medium is 1.4. Which of the following is the minimum internal angle for total internal reflection to take place in the medium?

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An engine raises 1000kg of water through a height of 60m in 20s. What is the power of the engine? (Take g = 10ms^-2>).

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The power of an engine is the rate at which it does work. We can use the formula P = W/t, where P is the power, W is the work done and t is the time taken. In this question, the work done is the product of the force applied and the distance moved in the direction of the force. Since the engine is raising a mass of 1000kg, the force applied is equal to the weight of the water, which is given by F = m*g, where m is the mass and g is the acceleration due to gravity. Thus, F = 1000kg * 10m/s^2 = 10,000N. The distance moved by the water is the height through which it is raised, which is 60m. Therefore, the work done by the engine is given by W = F*d = 10,000N * 60m = 600,000J. Finally, we can substitute these values into the power formula to obtain P = W/t = 600,000J / 20s = 30,000W. Therefore, the power of the engine is 30,000W. Answer: 30,000 W.

The distance between a node and an anti-node for a transverse wave is equal to

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In a transverse wave, nodes are the points that do not move while the anti-nodes are the points of maximum displacement. The distance between a node and an adjacent anti-node is equal to one-fourth of the wavelength. This is because, in one complete cycle of the wave, there is one node and one anti-node, and the distance between them is half a wavelength. Thus, the distance between a node and an anti-node is one-fourth of a wavelength. Therefore, the correct option is "one-fourth of the wavelength."

Which of the following is not a property of longitudinal waves?

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The property that is not associated with longitudinal waves is polarization. Longitudinal waves are waves in which the oscillations of the particles of the medium are in the same direction as the direction of wave propagation. In other words, the wave moves parallel to the oscillations of the particles. Examples of longitudinal waves include sound waves and seismic waves. Compression is a property of longitudinal waves in which the particles of the medium are pushed together, while rarefaction is when the particles are spread apart. Reflection is the property where a wave bounces back after hitting a boundary. Refraction is the property where a wave bends as it passes from one medium to another. Diffraction is the property where a wave bends around a barrier or through an opening.

Which of the following instruments can be used to compare the relative magnitudes of charges on two given bodies?

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The instrument that can be used to compare the relative magnitudes of charges on two given bodies is the gold-leaf electroscope. The gold-leaf electroscope works by using two thin gold leaves suspended from a metal rod within a glass container. When a charged object is brought near the metal rod, the charges induce a separation of charges in the gold leaves, causing them to repel each other and move apart. The amount of separation of the leaves is proportional to the magnitude of the charge on the object. To compare the charges on two bodies, you would first bring one body near the metal rod and observe the amount of separation of the leaves. Then, you would discharge the electroscope by touching the metal rod with your hand, and repeat the process with the other body. By comparing the amount of separation of the leaves in each case, you can determine which body has the greater charge. The other options listed are not directly used to compare charges on two bodies. The electrophorous is used to generate a static charge on an object, the ebonite rod can be charged by rubbing it with fur or silk, the proof plane is used to transfer charge to the gold-leaf electroscope, and the capacitor is used to store electrical charge.

The image in a pine-hole camera is always

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The image in a pinhole camera is always inverted. This is because the light passing through the small hole in the camera travels in straight lines and forms an inverted image on the opposite side of the camera. The size of the image depends on the size of the hole, the distance between the hole and the image plane, and the distance between the object and the hole. However, the image is always inverted regardless of these factors.

Water in an open container boils at a lower temperature when heated at the top of a mountain than at sea-level because at the top of a mountain the

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Water in an open container boils when the vapor pressure of the water equals the atmospheric pressure. At higher altitudes, the atmospheric pressure is lower than at sea-level because the column of air above is shorter. As a result, water boils at a lower temperature at higher altitudes because the lower pressure means that water molecules need less thermal energy to break the intermolecular bonds and evaporate into the air. Therefore, the correct option is that at the top of a mountain, the pressure is lower than that at sea-level, leading to a lower boiling point of water.

The motion of the prongs of the sounding tuning fork is

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The motion of the prongs of a sounding tuning fork is vibratory. When the prongs are struck or set into vibration, they oscillate back and forth in opposite directions, creating a series of compressions and rarefactions in the surrounding air molecules. This causes the air molecules to vibrate and propagate sound waves through the air, which we perceive as sound. The vibratory motion of the prongs is what sets up the sound wave, which is why tuning forks are often used as a reference pitch for tuning musical instruments.

Calculate the heat energy required to vapourize 50g of water initially at 80^oC if the specific heat capacity of water is 4.2Jg^-1K (specific latent heat of vapourization of water is 2260Jg^-1).

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To calculate the heat energy required to vaporize 50g of water initially at 80^oC, we need to first calculate the amount of heat energy required to raise the temperature of the water from 80^oC to its boiling point, which is 100^oC. Using the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature, we have: Q₁ = (50g)(4.2Jg^-1K)(100^oC - 80^oC) = 4200J The amount of heat energy required to vaporize the water at its boiling point can be calculated using the formula Q = mL, where Q is the heat energy, m is the mass, and L is the specific latent heat of vaporization. We have: Q₂ = (50g)(2260Jg^-1) = 113000J Therefore, the total amount of heat energy required to vaporize 50g of water initially at 80^oC is: Q_total = Q₁ + Q₂ = 4200J + 113000J = 117200J Thus, the answer is 117200J.

Which of the following is NOT a vector quantity?

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Temperature is NOT a vector quantity. Vector quantities have both magnitude and direction, whereas scalar quantities have only magnitude. Momentum, force, velocity, and displacement are all vector quantities because they have both magnitude and direction. Temperature, on the other hand, only has a magnitude (e.g. 25 degrees Celsius), and does not have a direction. Therefore, temperature is a scalar quantity.

Which of the following substance is not a good conductor of electricity?

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Glass is not a good conductor of electricity. This is because glass is an insulator and has very few free electrons that can move and conduct electricity. In contrast, metals such as aluminium and copper are good conductors of electricity because they have many free electrons that can move freely and carry an electric current. The human body and the Earth can also conduct electricity, although their conductivity is lower than that of metals.

Which of the followiempeng statements is/are not correct?

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In a wave the maximum displacement of particles from their equilibrium positions is called.

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In a wave, the maximum displacement of particles from their equilibrium positions is called the amplitude. The amplitude represents the maximum height of a wave or the distance between the crest (highest point) and the trough (lowest point) of a wave. It is a measure of the wave's energy, and the greater the amplitude, the more energy the wave carries. For example, in a sound wave, the amplitude determines the loudness of the sound, and in a light wave, it determines the brightness of the light.

A stone tied to a string is made to revolve in a horizontal circle of radius 4m with an angular speed of 2 rad per sec. With what tangential velocity will the stone move off the circle if the string is cut?

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The tangential velocity of a circular motion is given by the product of the radius and the angular velocity. When the string is cut, the centripetal force acting on the stone is removed, and the stone moves off the circle with the same tangential velocity. So, the tangential velocity of the stone when the string is cut is: v = rω = 4m × 2 rad/s = 8 m/s Therefore, the answer is 8.0 ms^-1.

A thermometer has its stem marked in millimeter instead of degree Celsius. The lower fixed point is 30mm and the upper is 180mm. Calculate the temperature in degree celsius when the thermometer reads 45mm.

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All the heat generated by a current of 2A passing through a resistor of 6Ω for 2.5s is used to evaporate 5 g of a liquid at its boiling point. What is the specific latent heat of the liquid?

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The heat generated by the current passing through the resistor is given by the formula H = I²RT, where H is the heat energy, I is the current, R is the resistance, and T is the time for which the current flows. In this case, I = 2A, R = 6Ω, and T = 2.5s. So, the heat generated is: H = (2A)² x 6Ω x 2.5s = 60J This heat is used to evaporate 5g of a liquid at its boiling point. The specific latent heat of vaporization (L) of the liquid is given by the formula: L = H/m where m is the mass of the liquid. In this case, m = 5g, so: L = 60J / 5g = 12J/g Therefore, the specific latent heat of the liquid is 12J/g. The option closest to this value is 120 Jg^-1, so that would be the answer.

A boy pulls a nail from the wall with a string tied to the nail. The string is inclined at an angle of 60^o to the wall. If the tension in the string is 4N, what is the effective force used in pulling the nail?

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A short chain is usual attached to the back of a petrol tanker trailing behind it to ensure that the

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The correct option is: charges generated by friction in the tanker can be conducted to the earth. The short chain is usually made of metal and is attached to the back of a petrol tanker trailing behind it to prevent the buildup of static electricity caused by friction between the tanker and the road surface. As the tanker moves, friction between the wheels and the road generates static electricity, which can accumulate on the metal body of the tanker. If the static charge buildup is not dissipated, it can cause a spark, which can ignite the fuel vapor, leading to an explosion. The short chain attached to the tanker helps to conduct the static charge to the earth, reducing the risk of explosion.

What is the gravitational potential due to a molecule of mass, m and at a distance, r from it? (G = gravitational constant).

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The gravitational potential due to a molecule of mass, m and at a distance, r from it is given by the formula: Gm/r. The gravitational potential is a measure of the work done per unit mass in moving an object from infinity to a point in the gravitational field. Gravitational potential energy is the energy associated with an object due to its position in a gravitational field. The higher the gravitational potential energy, the more work is required to move the object against the force of gravity. The formula for gravitational potential due to a point mass is a simple expression of the strength of the gravitational field created by a mass at a distance r. This formula is widely used in physics to calculate the gravitational potential at a point due to a body of mass m.

Calculate the escape velocity for a rocket fired from the earth's surface at a point where the acceleration due to gravity is 10ms^-2 and the radius of the earth is 6 x 10⁶m.

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Which of the following is a stringed instrument?

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A stringed instrument produces sound through the vibration of its strings, which are usually stretched between two points. The sound is amplified through a resonating chamber. Therefore, the stringed instrument among the options listed is the piano. The piano has strings that are struck by hammers when the keys are pressed, producing different notes and sounds.

A sound pulse sent vertically downwards into the earth is reflected from two different layers of the earth such that echoes are heard 1.2s and 1.4s. Assuming speed of the pulse is 2000ms^-1, calculate the distance between the layers.

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When the sound pulse is sent vertically downwards into the earth, it is reflected from the two layers and returns back to the surface. The time interval between the two echoes is the time taken by the pulse to travel from the first layer to the second layer and back. Let's assume that the distance from the surface to the first layer is 'd' meters and the distance between the first and second layer is 'x' meters. The total distance covered by the pulse would be equal to the sum of the distance travelled to reach the first layer, the distance travelled between the two layers, and the distance travelled to return to the surface. Total distance = d + 2x Using the formula for speed, distance and time, we can express the time taken for the pulse to travel to the first layer and back as: 2d/2000 Similarly, the time taken for the pulse to travel to the second layer and back can be expressed as: 2(d + x)/2000 Given that the time interval between the two echoes is 0.2s, we can set up the following equation: 2(d + x)/2000 - 2d/2000 = 0.2 Simplifying this equation, we get: d + x - d = 200 x = 200m Therefore, the distance between the two layers is 200m. Thus, option A is the correct answer.

A block of material of volume 20cm^-3 and density 2.5gcm^-3 is suspended from a spring balance with half the volume immersed in water. What is the reading of the spring balance? (Density of water = 1.0gcm^-3).

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Which of the following is a derived unit?

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A derived unit is a unit of measurement that is derived from the seven base units of the International System of Units (SI). The base units are the units for length, mass, time, electric current, temperature, amount of substance, and luminous intensity. The units of metre, kilogram, second and ampere are base units, whereas the unit of coulomb is a derived unit, defined as the quantity of electric charge transported by a constant current of one ampere in one second. Therefore, the correct answer is Coulomb.

Which of the following surfaces will radiate heat energy best?

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Black surfaces will radiate heat energy best. This is because black surfaces absorb all wavelengths of light and reflect very little, which means they absorb more heat and therefore radiate more heat energy. White and light-colored surfaces reflect most of the incoming light, and absorb less heat energy. On the other hand, dark colors, especially black, absorb more light and heat energy, which makes them better radiators of heat. Therefore, black surfaces are considered to be the best radiators of heat energy among the given options.

Which of the following is not a consequence of a force field?

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A ray of light is incidence on a plane mirror at an angle of 35^o. What is the angle by the reflected ray with the surface of the mirror?

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A string is stretched between two points 50cm apart. It is then plucked at its center and the velocity of the wave produced is 300m/s. Calculate the number of vibrations made by the string in 1s.

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The velocity of a wave, v is given by v = fλ, where f is the frequency of the wave and λ is the wavelength. For a standing wave in a string, the wavelength λ is equal to twice the length of the string, since it is fixed at both ends. Therefore, λ = 2 × 50 cm = 100 cm = 1 m The velocity of the wave is given as 300 m/s. So, 300 m/s = f × 1 m Hence, frequency f = 300 Hz The number of vibrations (cycles) per second is equal to the frequency of the wave, therefore the number of vibrations made by the string in 1s is 300. Therefore, the answer is 300 vibrations per second.

A piece of cork floating on water is acted upon by the forces of...

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A block of ice at its melting point is left on a table in the atmosphere and observed to melt gradually. Which of the following statements is true about the melting process?

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Which of the following is used to determine the relative density of the acid in a car battery?

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A hydrometer is used to determine the relative density of the acid in a car battery. A hydrometer is a device that measures the specific gravity or relative density of a liquid. The acid in a car battery is a mixture of sulfuric acid and water, and its density changes with the state of charge of the battery. A hydrometer can be used to measure the relative density of the acid, which provides an indication of the state of charge of the battery. When the battery is fully charged, the acid has a higher density than when it is discharged. Therefore, by measuring the relative density of the acid, it is possible to determine the state of charge of the battery.

(a) State the laws of electromagnetic induction.

(b) (i) Describe a simple experiment to show how an induced e.m.f, can be produced; (ii) State two factors on which the magnitude of the induced e.m.f. depends

(c) Explain what is meant by the r.m.s. value of an alternating current

(d) (i) If the alternating current is represented by \(I = l_{o} \sin \omega t\), state what the symbol \(I, I_{o}, \omega\) and \(\omega t\)represent.

(ii) Calculate the instantaneous value of such a current, if in a circuit it has r.m.s value of 15.0A when its phase angle is 30°. 

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(a) What is meant by the statement: The linear expansivity of a solid is \(1.0 \times 10^{-5}K^{-1}\)?

(b)(i) Describe an experiment to determine the linear expansivity of a steel rod. (ii) Steel bars, each of length 3m at 29°C are to be used for constructing a rail line. If the linear expansivity of steel is \(1.0 \times 10^{-5}K^{-1}\), calculate the safety gap that must be left between successive bars if the highest temperature expected is 41°C.

(c) State three advantages and two disadvantages of thermal expansion of solids. 

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(a)(i) Explain the terms: photoelectric emission and threshold frequency; (ii) Einstein's photoelectric equation can be written as \(E = hf - hf_{o}\) What does each of the symbols used in the equation above represent?

(b) Calculate the frequency of the proton whose energy is required to eject a surface electron with a kinetic energy of \(1.97 x 10^{-16} eV\) if the work function of the metal is \(1.33 x 10^{-16}eV\). \((1 eV = 1.6 x 10^{-18}J; h = 6.60 x 10^{-34}JS)\).

(c) In a photoelectric cell, no electrons are emitted until the threshold frequency of light is reached. Explain what happens to the energy of the light before emission of electrons begins. State one factor that may affect the numbers of emitted electrons.

(d) Explain what is meant by the duality of matter, illustrating your answer with observation phenomena. 

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(a) What is a wave motion?

The equation \(y = A \sin \frac{2\pi}{\lambda} (Vt-X)\) represents a wavetrain in which y is the vertical displacement of a particle at distance X from the origin in the medium through which the wave is travelling. Explain, with the aid of a diagram, what A and \(\lambda\) represent.

(b) (i) Describe an experiment to determine the frequency of a note emitted by a source of sound

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

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

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