WAEC SSCE - Physics - 2011

Total internal reflection occurs in an optical prism when light rays

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Total internal reflection occurs in an optical prism when light rays are incident in the prism at an angle greater than the critical angle. When a light ray travels from an optically denser medium (like a glass prism) to a less dense medium (like air), it bends away from the normal line. As the angle of incidence increases, the angle of refraction also increases until it reaches a certain angle called the critical angle. If the angle of incidence is greater than the critical angle, the light ray is totally reflected back into the denser medium, which is known as total internal reflection. This phenomenon is used in various optical devices such as prisms, optical fibers, and reflecting telescopes.

The image formed by a convex mirror is always

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The image formed by a convex mirror is always virtual, erect and diminished. A convex mirror is a diverging mirror, meaning that it spreads out the light rays that enter it. The image formed by a convex mirror is virtual, which means that it cannot be projected onto a screen. It is always upright or erect, which means that it is not inverted like the image formed by a concave mirror. The image formed by a convex mirror is always smaller than the object, hence diminished.

The area under a velocity-time graph represents

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The area under a velocity-time graph represents the distance covered by an object. Velocity is the rate of change of displacement with time. Therefore, the area under the velocity-time graph is equal to the displacement covered by the object during the given time interval. This is because the area under the graph is the product of the time interval and the average velocity during that time interval, which is equal to the distance traveled. So, the correct option is "distance covered".

A body of mass 120g placed at the 10cm mark on a uniform metre rule makes the rule settle horizontally on a fulcrum places at 35cm mark. Calculate the mass of the rule

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A coin is pushed from the edge of a laboratory bench with a horizontal velocity of 15.0 ms^-1. If the height of the bench from the floor is 1.5m, calculate the distance from the foot of the bench to the point of impact with the floor [g = 10ms^-2]

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We can solve this problem using kinematic equations of motion. Since the motion is projectile motion, we can break it into two components, horizontal and vertical. In the horizontal direction, there is no acceleration, so the velocity remains constant throughout the motion. In the vertical direction, the coin is moving upward against the force of gravity, which causes it to slow down, then come to rest at the highest point before falling downward. The time taken to reach the highest point can be calculated using the vertical component of the initial velocity and acceleration due to gravity. Using the equation: v = u + at where: v = final velocity = 0 (at the highest point) u = initial velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to reach the highest point Solving for t, we get: t = u/a = 15.0/10 = 1.5s The maximum height reached by the coin can be calculated using the equation: s = ut + 0.5at^2 where: s = maximum height reached u = initial vertical velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to reach the highest point = 1.5s Solving for s, we get: s = 0 + 0.5 x 10 x (1.5)^2 = 11.25m Now, the coin falls from the maximum height and hits the floor. The time taken to fall from the maximum height can be calculated using the equation: s = ut + 0.5at^2 where: s = height of the bench = 1.5m u = initial vertical velocity = 0 a = acceleration due to gravity = 10 ms^-2 t = time taken to fall from maximum height Solving for t, we get: 1.5 = 0 + 0.5 x 10 x t^2 t^2 = 0.3 t = sqrt(0.3) = 0.55s (ignoring the negative root) Now, we can calculate the horizontal distance traveled by the coin during the time it was in the air using the equation: s = ut + 0.5at^2 where: s = horizontal distance traveled u = initial horizontal velocity = 15.0ms^-1 a = acceleration in horizontal direction = 0 (no acceleration) t = time taken to fall from maximum height = 0.55s Solving for s, we get: s = 15.0 x 0.55 = 8.25m Therefore, the distance from the foot of the bench to the point of impact with the floor is approximately 8.25m. Answer: 8.22m (rounding off to two decimal places)

The focal length of the eye-piece of an astronomical telescope is f₁, while the focal length of the object is f₂. Fro normal adjustment, the angular magnification is given by

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The change in mass of fuel during a nuclear reaction is 2.0 x 10^-27 kg. Calculate the amount of energy released. (Speed of light = 2.0 x 10⁸ms^-1)

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The equation that relates mass and energy is E=mc². Here, the change in mass is given as 2.0 x 10^-27 kg. The speed of light is given as 2.0 x 10⁸ ms^-1. Substituting these values in the equation, we get: E = (2.0 x 10^-27 kg) x (2.0 x 10⁸ ms^-1)² E = 1.8 x 10^-10 J Therefore, the amount of energy released is 1.8 x 10^-10 J.

Which of the following statements about the electromagnetic waves is correct?

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Using the circuit diagram above. Calculate the total charge in the circuit

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Which of the following assumptions is not valid for an ideal gas ?

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The assumption that is not valid for an ideal gas is that the "force of attraction between molecules is negligible." This assumption is not valid for real gases since molecules have intermolecular forces of attraction. In an ideal gas, it is assumed that the gas particles have no intermolecular forces of attraction, meaning that they do not attract or repel each other, and they move independently. However, in reality, all gases have some degree of intermolecular forces of attraction.

Which of the following statements correctly defines a simple machine? A device

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The correct statement that defines a simple machine is: "a device with which work can be done easily". A simple machine is any mechanical device that can change the magnitude or direction of an applied force, making it easier to move or lift an object. Examples of simple machines include levers, pulleys, inclined planes, screws, and wheel and axle systems. These machines work by reducing the amount of force required to do a certain amount of work, allowing humans to accomplish tasks that would otherwise be difficult or impossible to perform. Therefore, option C is the correct answer.

Presbyopia is a defect of the eye resulting from

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Two simple pendulum A and B of equal lengths and of masses 5g and 20g respectively are located in the same environment. The periods TA and TB of their respective oscillations are related by the equations

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The main difference between echo and reverberation is that

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Which of the following propeties is not considered in choosing mercury as a thermomemetric liquid?

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The density P of a spherical ball of diameter d and mass m is given by

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Nuclear fusion is not used as a source of enegy because

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An object of mass 5.0 kg moves with a velocity of 10ms^-1. Calculate its momentum.

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The momentum of an object is defined as the product of its mass and velocity. Mathematically, this can be expressed as p = mv, where p is momentum, m is mass and v is velocity. Using the given values, we can calculate the momentum of the object as follows: p = mv = 5.0 kg x 10ms^-1 = 50.0 kgms^-1 Therefore, the momentum of the object is 50.0 kgms^-1. Answer: 50.0 kgms^-1

An object is placed 20.0cm in front of a converging lens of focal length 15.0cm. Calculate its image distance

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The formula to calculate the image distance for a converging lens is: 1/f = 1/do + 1/di where f is the focal length of the lens, do is the distance of the object from the lens, and di is the distance of the image from the lens. Substituting the given values: 1/15 = 1/20 + 1/di Simplifying and solving for di: di = 60 cm Therefore, the image distance is 60.0cm. Answer: Option D.

A metal of mass 200g at a temperature of 100^oC is placed in 100g of water at 25^oC in a container of negligible heat capacity. If the final steady temperature is 30^oC, calculate the specific heat capacity of the metal. [specific heat capacity of the water is 4200 Jkg^-1 K^-1]

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When the pointed end of an uncharged optical pin is brought near the cap cf a positively charged electroscope, it is observed that the gold

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A hypsometer is used for determining

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The capacitance of a parallel-plate capacitor

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The capacitance of a parallel-plate capacitor is the ratio of the magnitude of the charge on either plate to the potential difference between them. The capacitance is directly proportional to the area of the plates and inversely proportional to the distance between them. Thus, as the separation between the plates decreases, the capacitance increases. The capacitance is also directly proportional to the permittivity of the dielectric material between the plates. A dielectric is an insulating material that can be placed between the plates of a capacitor to increase its capacitance. The permittivity of the dielectric material is a measure of its ability to store electrical energy in an electric field. Thus, adding a dielectric between the plates of a parallel-plate capacitor increases the capacitance. Therefore, the correct answer is: the capacitance of a parallel-plate capacitor is greater with a dielectric material between the plates than without a dielectric.

Which of the following statements about anomalous expansion of water are correct? i. There is contraction between 0^oC and 4^oC. ii. There is expansion between 0^oC and 100^oC. iii. The volume is minimum at 4^oC. iv. The volume is maximum at 4^oC

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Ether produces a cooling effect when it is poured on the hand because it has

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Ether produces a cooling effect when it is poured on the hand because it has a high latent heat of vaporization. Latent heat is the energy absorbed or released during a phase change. When ether is poured on the hand, it quickly evaporates due to its low boiling point. As it evaporates, it absorbs heat energy from the hand to overcome the intermolecular forces holding the liquid together, causing a cooling effect on the skin. The higher the latent heat of vaporization, the greater the cooling effect. Therefore, "high latent heat of vaporization" is the correct answer.

The unit of capacitance is

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The unit of capacitance is farad, which is represented by the symbol F. Capacitance is the ability of a capacitor to store electric charge per unit voltage applied. One farad of capacitance is defined as the capacitance of a capacitor that stores one coulomb of charge when a potential difference of one volt is applied across it. In simpler terms, it is a measure of the amount of electrical charge that can be stored in a capacitor for a given voltage.

A metal rod of density 7000 kgm^-3 and cross-sectional area of 0.001257m² has a mass of 1.76kg. Calculate its length.

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two sound waves have frequencies of 12Hz and 10Hz. Calculate their beats period

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When two sound waves of different frequencies overlap, they interfere with each other to produce a resultant wave. If the frequencies of the two waves are close, a phenomenon called beats occurs, where the amplitude of the resultant wave varies periodically. The period of beats is given by T = 1/(f1 - f2), where f1 and f2 are the frequencies of the two waves. Using the formula, we can calculate the beats period for the given frequencies: T = 1/(12 Hz - 10 Hz) = 1/2 Hz = 0.5 s Therefore, the answer is 0.5s.

Which of the following statements about the image formed by a plane mirror is not correct?

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The correct option is: "it is formed by actual intersection of rays." Explanation: When an object is placed in front of a plane mirror, its image is formed behind the mirror. The image formed is virtual, which means that it cannot be projected onto a screen. It is laterally inverted, which means that left appears as right and right appears as left. The size of the image is the same as that of the object, and therefore, it has unit magnification. The distance of the image from the mirror is the same as the distance of the object from the mirror, and therefore, the last statement is also true. However, the image is not formed by actual intersection of rays as the rays of light do not actually converge at the position of the image. The image is formed due to the reflection of light from the mirror's surface.

A wire of length 30cm is moved with a speed of 2ms^-1 at right angles to a magnetic field of flux density 0.4T. calculate the emf induced in the wire

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The emf induced in a wire moving at right angles to a magnetic field is given by the equation: emf = B × l × v where B is the magnetic flux density, l is the length of the wire, and v is the velocity of the wire. Plugging in the given values, we have: emf = 0.4T × 0.3m × 2ms^-1 = 0.24V Therefore, the emf induced in the wire is 0.24V. The correct option is: 0.24V

The radius of a wheel is 30.0 cm and that of its axle is 6.0cm. Calculate the effort required to lift a load of 120.0N using this machine. Assuming 100% efficiency

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This is a problem involving the mechanical advantage of a simple machine. The machine in question is a wheel and axle. The effort required to lift a load is dependent on the mechanical advantage of the machine. The mechanical advantage of a wheel and axle is the ratio of the radius of the wheel to the radius of the axle. In this case, the mechanical advantage is: MA = radius of wheel / radius of axle = 30 cm / 6 cm = 5 This means that for every unit of effort applied to the machine, it can lift 5 units of load. Using this information, we can determine the effort required to lift a load of 120.0 N by setting up the equation: MA = load / effort Solving for effort, we get: effort = load / MA = 120.0 N / 5 = 24.0 N Therefore, the effort required to lift a load of 120.0 N using this machine with 100% efficiency is 24.0 N. The correct answer is (c) 24.0N.

The correct relationship between "G" and "g" in a gravitational field is given by the equation (Where the symbols have their usual meanings)

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The correct relationship between "G" and "g" in a gravitational field is given by the equation g = \(\frac{GM}{R^2}\), where g represents the acceleration due to gravity, G is the gravitational constant, M is the mass of the attracting body, and R is the distance between the centers of mass of the two objects. This equation is known as Newton's law of gravitation and states that the force of attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The acceleration due to gravity at any point is the gravitational force experienced by a unit mass at that point. The gravitational constant G is a fundamental constant of nature and is considered to be one of the most accurately measured physical constants.

Which of the following practices will lead to losses in electrical power transmission?

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An ammeter with a full scale deflection of 10mA has an internal resistance 0.5\(\Omega\). calculate the resistance of the shunt required to adapt it to read up to 3A

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The speed of light in a certain medium is V while its speed in a vacuum is C. The absolute refractive index of the medium is

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The absolute refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium. Therefore, the formula for the absolute refractive index of the medium is: \[\text{Absolute refractive index} = \frac{\text{Speed of light in vacuum}}{\text{Speed of light in the medium}} = \frac{C}{V}\] Therefore, the answer is \(\frac{C}{V}\).

The pressure in a liquid

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Which of the following properties is not applicable to X-rays? They

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X-rays are electromagnetic waves that are produced when high-speed electrons are stopped by a metal target. They have many useful properties such as traveling in straight lines, traveling at the speed of light, and affecting photographic films. X-rays, however, are not affected by magnetic fields, meaning they cannot be deflected by a magnetic field. Therefore, the property that is not applicable to X-rays is that they are deflected by magnetic fields.

The property of a fluid that is used to determine its suitability as a lubricant is its

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The property of a fluid that is used to determine its suitability as a lubricant is its viscosity. Viscosity is a measure of a fluid's resistance to flow or deformation, and it is directly related to its thickness or consistency. The thicker the fluid, the higher its viscosity, and the more effective it is at providing lubrication and reducing friction between two surfaces. Therefore, high viscosity fluids are preferred as lubricants since they provide better lubrication, while low viscosity fluids are preferred as coolants.

A ray undergoes a minimum deviation at 40^o when it is incident on equilateral triangular glass prism. Calculate the refractive index of the prism

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In the absence of gravitational force, the weight of the body is

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In the absence of gravitational force, the weight of the body is zero. This is because weight is the force with which a body is attracted towards the center of the Earth or any other massive body. In the absence of such a force, the body will not experience any weight. However, the mass of the body remains the same, as it is a measure of the amount of matter contained in the body. Therefore, - zero - is the correct answer.

The resistivity, \(\mathit{P}\), of a material of length l, cross-sectional area A, resistance R, is given by the equation

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The resistivity, \(\mathit{P}\), of a material is a measure of its ability to resist the flow of electric current. The resistance, R, of a material is directly proportional to its length, l, and inversely proportional to its cross-sectional area, A. Therefore, we can say that \(\mathit{P} = \frac{RA}{l}\), as this equation combines the resistance, length, and cross-sectional area to give the resistivity of the material.

Uranium-234 disintegrated to form Thorium-230 by emitting

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Uranium-234 and Thorium-230 are both radioactive isotopes, meaning they undergo spontaneous nuclear decay. In this case, Uranium-234 disintegrates to form Thorium-230 by emitting an alpha particle. An alpha particle is a helium nucleus, consisting of two protons and two neutrons, which is ejected from the nucleus during alpha decay. This results in the atomic number of the daughter nucleus being reduced by 2 and the mass number being reduced by 4. So, is correct.

Which of the following statements is not correct?

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The statement that is not correct is: "molecules of ice, water and water vapour have equal intermolecular distances." Explanation: - Ice, water, and water vapour are different states of water. They have different intermolecular distances because the intermolecular forces between their molecules are different. - In ice, the intermolecular forces are the strongest due to hydrogen bonding, which results in a rigid and orderly arrangement of water molecules with a fixed intermolecular distance. - In liquid water, the intermolecular forces are weaker than in ice, and the intermolecular distance is more variable. - In water vapour, the intermolecular forces are weakest among the three, and the intermolecular distance is the largest. Therefore, the statement that molecules of ice, water and water vapour have equal intermolecular distances is not correct.

For photoelectric emission, the threshold frequency is the

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The threshold frequency in photoelectric emission is the minimum frequency of incident radiation required to eject electrons. This means that if the frequency of the incident radiation is below the threshold frequency, no electrons will be emitted, regardless of the intensity or duration of the radiation. However, if the frequency of the incident radiation is equal to or greater than the threshold frequency, electrons will be emitted, and their kinetic energy will increase with increasing frequency. Therefore, the correct option is "minimum frequency of incident radiation required to eject electrons."

A stone of mass 300g is released from rest from the top of a bulding of height 100m. Determine the kinetic energy gained by the stone when it is a quarter way down from the point of release.[g = 10 ms^-2]

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A body is pulled over a distance of 500m by a force of 20N. If the power developed is o.4 kW, calculate the time interval during which the force is applied

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Power, P = work done (W) / time interval (t) We know that, work done (W) = force (F) x distance (d) Therefore, power (P) = (F x d) / t Rearranging this equation, we get: t = (F x d) / P Substituting the given values, we get: t = (20 N x 500 m) / 0.4 kW t = 25,000 s Therefore, the time interval during which the force is applied is 25,000 seconds. Answer: 25.0s

Which of the following equations shows how how the linear expansivity (\(\alpha\)) and the cubic expansivity (\(\gamma\)) of a material are related?

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Using the circuit diagram above. Calculate the potential difference across the capacitors in parallel

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Which of the following substances does not conduct electricity?

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Explain why water in a narrow glass tube has a concave meniscus while mercury, in the same tube, has a convex meniscus.

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(a)(i) State two advantages of alcohol over mercury as a thermometric liquid.

(ii) When the bulb of a thermometer is placed in a beaker of hot water, the level of the mercury first falls and then rises gradually. Explain this observation.

(b) List two factors, other than temperature, that affect the rate of evaporation of a liquid.

(b) A block of lead of mass 100 kg in a crucible and at a temperature of 40 °C was placed in an electric furnace rated 10 kW. If the melting point of lead is 320 °C, calculate the:

(i) quantity of heat required to heat the lead to its melting point;

(ii) additional heat energy required to melt the lead;

(iii) time taken to supply this additional energy. (Specific heat capacity of lead = 120 Jkg\(^{-1}\) K\(^{-1}\) (Specific Idtent heat of fusion lead = 2.5 x 10\(^{4} JK^{-1}\))

(d) State two precautions necessary in an experiment to determine the specific latent heat of vaporization of water.

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(a) Explain the terms:

(i) transmutation as it relates to radioactivity; (ii) stopping potential.

(b) \(^{23}_{11}A + ^2_1B\) —> \(^p_qC\) + proton

\(^p_qC\) —> \(^r_sE\) + beta

A nucleus C, formed artificially from A and B radioactive and quickly decays to another nucli E as indicated in the nuclear equations abc Datermine the values of p, q, r and s.

(c) A certain metal of work function 1.6 eV is irradiated with ultra-violet light of wavelength 3.6 x 10\(^{-7}\) Calculate the maximum

(i) kinetic energy of ejected electron in joules;

(ii) speed of an emitted electron. (1eV = 1.6 x 10\(^{-18}\) J; C = 3.0 x 10\(^{8}\) ms\(^{-1}\); m, = 9.1 x 10\(^{-31}\) kg; h = 6.6 x 10\(^{-34}\) Js)

(d) If source of the ultra-violet light in (c) above is mo away from the surface of the metal, state the of on the maximum speed of the ejected electron

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TEST OF PRACTICAL KNOWLEDGE QUESTION

Use the diagram above as a guide to carry out the following experiment.

1. Trace the outline ABCD of the rectangular glass prism on the drawing paper provided.
2. Remove the prism. Select a point N on AB such that AN is about one-quarter of AB.
3. Draw the normal LNM. Also, draw a line RN to make an angle \(\theta\) = 75° with AB at N.
4. Fix two pins at P\(_{1}\) and P\(_{2}\) on line RN. Replace the prism on its outline.
5. Fix two other pins at P\(_{3}\) and P\(_{4}\) such that they appear to be in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\) when viewed through the prism from DC.
6. (vi) Remove the prism and the pins at P\(_{3}\) and P\(_{4}\). Draw a line to join P\(_{3}\) and P\(_{4}\) 
7. Produce line P\(_{4}\) P\(_{3}\) to meet the line DC at O. Draw a line to join NO.
8. Measure and record the values of MO and NO.
9. Evaluate \(\theta\) = \(\frac{MO}{NO}\) and cos \(\theta\).
10. Repeat the procedure for four other values of \(\theta\) = 65° 55°, 45°, and 35°. In each case, evaluate \(\theta\) and cos \(\theta\).
11. Tabulate your readings.
12. Plot a graph with cos \(\theta\) on the vertical axis and \(\theta\) on the horizontal axis.
13. Determine the slope, s, of the graph.
14. State two precautions taken to ensure accurate results

(b)i. State Snell's law of refraction.

ii. Calculate the critical angle for the glass prism used in the experiment above if its refractive index is 1.5.

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with a wooden block to which a hook is fixed, a set of masses, spring balance, and other necessary materials. Using the diagram above as a guide, carry out the following instructions.

1. Record the mass m\(_{0}\), indicated on the wooden block.
2. Place the block on the table.
3. Attach the spring balance to the hook.
4. Pull the spring balance horizontally with a gradual increase in force until the block just starts to move Record the spring balance reading F.
5. Repeat the procedure by placing in turn mass m=200, 400, 600, and 800g on top of the block. In each case, read and record the corresponding value of F.
6. Evaluate M = m\(_{0}\) + m and R = \(\frac{m}{100}\) in each case
7. Tabulate your readings.
8. Plot a graph with F on the vertical axis and R on the horizontal axis
9. Determine the slope, s, of the graph.
10. State two precautions taken to ensure accurate results.

(b)i. Define coefficient of static friction. 

ii. A block of wood of mass 0.5 kg is pulled horizontally on a table by a force of 2.5 N. Calculate the coefficient of static friction between the two surfaces.(g = 10ms\(^{-2}\))

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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 of 25 m from the foot of the tower. Calculate the height of the tower. = 10 ms\(^{-2}\)]

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(a)(i) What is an eclipse?

(ii) List the three types of eclipse.

(b) A student in a lecture theatre can read from the board clearly but requires a pair of spectacles to read from a book.

(i) What eye defect has this student?

(ii) What type of lens is needed to correct the eye defect?

(iii) The focal length of the lens used to correct this defect is 10cm. Calculate the power of the lens.

(c) A car B moves towards a stationary car A. If B produces an ultrasonic sound at a point and it takes 5.6 x 10\(^{-3}\)s for a beep to be heard in B, calculate the distance between the two cars at that instant. (Speed. sound in air = 340 ms\(^-\))

(d) The image of an object is located 9 cm behind a convex mirror. If magnification produced is 0.6, calculate the focal length of the mirror.

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(a) Explain diffusion.

(b) Give one reason why the rate of diffusion is higher in gases than in liquids at the same temperature.

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An electron of charge 1.60 x 10\(^{-19}\) C is accelerated under a potential difference of 1.0 x 10\(^5\) V. Calculate the energy of the electron in joules.

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

(b) two uses of polaroids.

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(a). State: (a) two applications of electrolysis in an industry

(b) one application of electrolysis in a school laboratory.

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with cells, a potentiometer, an ammeter, a voltmeter, a bulb, a key, a jockey, and other necessary materials.

1. Measure and record the emf E of the battery. 
2. Set up a circuit as shown in the diagram above.
3. Close the key K and use the jockey to make a firm contact at J on the potentiometer wire such that PJ = x = 10cm.
4. Take the record of the voltmeter reading V and the corresponding ammeter reading I.
5. Evaluate log V and log I.
6. Repeat the procedure for other values of x =20, 30. 40, 50, and 60cm.
7. Tabulate your readings.
8. Plot a graph with the log I on the vertical axis and log V on the horizontal axis.
9. Determine the slope, s, of the graph.
10. Determine the intercept, c, on the vertical axis.
11. State two precautions taken to ensure accurate results.

(b)i. How is the brightness of the bulb affected as x increases? Give a reason for your answer.

ii. List two electrical devices whose actions do not obey ohm's law

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In fig. la and fig.1 b above, Ida and Wb represent the respective loads on a spring placedtiear a 30 cm rule, when in air and when in water:

(a) Identify the force causing a shrink in the spring in fig.(b).

(b) Given that the force constant of the spring is 2.0 x 10\(^{11}\) Nm\(^{-1}\), calculate the work done by the force in causing the shrink.

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State three methods of polarizing an unpolarized light

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State three properties of cathode rays which suggest the particle nature of matter

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