WAEC SSCE - Physics - 2015

Two strings each inclined at an angle 30o to the horizontal are used to hold a bucket of water weighing 20N. Calculate the tension i n each string.

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The diagram above illustrates a block ans tackle pulley system in which an effort E supports a load of 100.0N. If the efficiency of the machine is 75%, calculate the value of E

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An electric generator rated 12 kW, 2 kV distribute power through a cable of resistance 20\(\Omega\). Calculate the power loss in the cable.

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Which of the following statements about diode is correct?

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The slope of a straight-line velocity-time graph represents

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The slope of a straight-line velocity-time graph represents the uniform acceleration. In other words, if the graph is a straight line, the slope of the line represents the rate at which the velocity is changing, which is the acceleration. The steeper the slope, the greater the acceleration, while a zero slope represents zero acceleration, which means the velocity is constant. Therefore, is the correct answer: uniform acceleration.

In an experiment in which a molten substance is allowed to cool, the cooling curve above was obtained. The temperature 60^oC is known as the

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The cooling curve shows how the temperature of a substance changes over time as it cools down. The temperature at which a substance changes from a liquid to a solid is known as its melting point. In the given cooling curve, the temperature at which the slope of the curve changes is known as the melting point. Therefore, the correct answer is the melting point. So, the temperature 60oC is the melting point of the substance.

A swimming pool is 2.1m deep. If it contains water of refractive index 1.3, calculate the apparent depth of pool

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When light enters from one medium to another, its speed changes and it bends. This is called refraction. The refractive index (n) of a medium is the ratio of the speed of light in vacuum to the speed of light in the medium.

The formula for calculating the apparent depth (d') of an object in a medium is given as:

d' = d/n

where d is the actual depth of the object and n is the refractive index of the medium.

In this case, the actual depth of the pool is given as 2.1m and the refractive index of water is 1.3.

Therefore, the apparent depth of the pool can be calculated as follows:

d' = 2.1m / 1.3 = 1.6m

Thus, the apparent depth of the pool is 1.6m. Therefore, the correct option is C.

An alternating current supply is connected to an electric lamp which lights with the same brightness as it does with direct current source emf 6v. The peak potential difference of the a.c supply is

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A quantity of hot water at 100^oC is added to 400g of water at 10^oC until the temperature of the mixture is 60^oC.

Calculate the mass of the hot water added. [Specific heat capacity of water =4200JKg^-1 K^-1]

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A bullet fired vertically upwards reaches a height of 500m. Neglecting air resistance, calculate the magnitude of the initial velocity of the bullet. [g = 10ms^-2]

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When a bullet is fired vertically upwards, it will continue to move upward until the force of gravity acting downwards slows it down to a stop and then pulls it back down towards the ground. The maximum height the bullet reaches before it falls back down is called the maximum height or the vertex. At the maximum height, the final velocity of the bullet is zero, and the initial velocity is what we are required to find. We can use the equation of motion that relates the initial velocity, final velocity, acceleration and displacement to solve for the initial velocity. This equation is: v_f² = v_i² + 2as where v_f is the final velocity (zero), v_i is the initial velocity (what we want to find), a is the acceleration due to gravity (-10ms^-2 since it is acting in the opposite direction to the motion of the bullet), and s is the displacement (500m). Substituting the known values into the equation, we get: 0 = v_i² + 2(-10ms^-2)(500m) Simplifying, we get: v_i² = 10000 Taking the square root of both sides, we get: v_i = 100ms^-1 Therefore, the magnitude of the initial velocity of the bullet is 100.0ms^-1.

When an air column is set into vibrations, the distance between two consecutive nodes of the resultant wave is

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When an air column is set into vibrations, it produces sound waves which propagate through the air. In a stationary wave, nodes are the points that appear to be standing still and do not undergo any vibration. They are formed due to the interference between the incident wave and the reflected wave. The distance between two consecutive nodes of a stationary wave is half of the wavelength. This is because a node is formed at the point where the incident wave and reflected wave interfere destructively, resulting in a minimum amplitude or zero displacement. Thus, the distance between two consecutive nodes is equal to half the distance between a node and an antinode (the points of maximum amplitude or displacement), which is half of the wavelength. Therefore, the correct answer is "half of the wavelength".

When current flows through a moving-coil galvanometer, the force exerted on the pointer depends on the: i. strength of the current. ii. magnetic field strength. iii. length of the coil. Which of the statement(s) above is/are correct?

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\(^{226}_{88}Ra\) emits two alpha particles to produce polonium(po) nuclide. The correct formula for the nuclide?

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A body of mass 1000kg is released from a height of 10m above the ground. Determine its kinetic energy just before it strikes the ground .[g = 10ms^-2]

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All electromagnetic waves in a vacuum have the same

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All electromagnetic waves in a vacuum have the same speed. This is known as the speed of light, which is approximately 3.0 x 10⁸ meters per second. Regardless of their frequency or wavelength, all electromagnetic waves travel at this same speed in a vacuum, such as in outer space. This is a fundamental property of electromagnetic waves and is a cornerstone of modern physics.

In an experiment in which a molten substance is allowed to cool, the cooling curve above was obtained. The temperature 60^oC is known as the

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The cooling curve shows the temperature changes of a molten substance as it cools. As the molten substance cools, its temperature gradually decreases until it solidifies. The temperature at which the substance changes from liquid to solid state is known as its melting point. In the given cooling curve, the temperature at which the curve plateaus and changes direction from a downward slope to a horizontal line is around 60°C. Therefore, 60°C is the melting point of the substance being tested. Therefore, the correct answer is "melting point".

A girl standing some distance from the cliff claps her hands and hears the echo 0.8s later. calculate her distance from the cliff. [speed of sound in air = 320 ms^-1]

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When sound waves travel, they can bounce off surfaces and return to the listener's ear, creating an echo. The distance between the listener and the reflecting surface can be calculated from the time taken for the sound to travel to the surface and back, and the speed of sound. In this problem, the time taken for the sound to travel to the cliff and back (i.e., the time for the echo to be heard) is given as 0.8s. The speed of sound in air is given as 320 ms^-1. Let's call the distance between the girl and the cliff "d". When she claps her hands, a sound wave travels the distance "d" to the cliff and then back again to her ear, covering a total distance of 2d. The time taken for this round trip is equal to the time for the echo to be heard, which is 0.8s. So, we can use the formula: distance = speed x time to calculate the distance "d" between the girl and the cliff. Rearranging the formula, we get: distance = (speed x time) / 2 Substituting the values given in the problem, we get: distance = (320 ms^-1 x 0.8s) / 2 distance = 128m Therefore, the girl is 128 meters away from the cliff. So, the correct option is (b) 128m.

Water is unsuitable for use as a thermometric liquid because it

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The mass of the earth is 6.0 x 10²⁴kg and that of the moon is 7.0 x 10²²kg. If the distance between them is 4.0 x 10⁸m, calculate the force of attraction between them. [G = 6.7 x 10^-11Nm²kg^-2]

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The force of attraction between two masses is given by the formula: F = G(m1m2)/d^2 where: F = force of attraction G = gravitational constant (6.7 x 10^-11 Nm^2/kg^2) m1 = mass of the first object (in kg) m2 = mass of the second object (in kg) d = distance between the centers of the two objects (in meters) Given: Mass of the earth (m1) = 6.0 x 10^24 kg Mass of the moon (m2) = 7.0 x 10^22 kg Distance between them (d) = 4.0 x 10^8 m Gravitational constant (G) = 6.7 x 10^-11 Nm^2/kg^2 Substituting the values into the formula: F = G(m1m2)/d^2 F = 6.7 x 10^-11 x (6.0 x 10^24) x (7.0 x 10^22) / (4.0 x 10^8)^2 F = 1.8 x 10^20 N Therefore, the force of attraction between the earth and the moon is 1.8 x 10^20 N. Answer option (D) is correct.

in a nuclear fission process, the mass defect was 1.2 x 10^-5kg. Calculate the energy released. [speed of the light in vacuum = c = 3.0 x 10⁸ms^-1]

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The energy released in a nuclear fission process can be calculated using Einstein's famous equation E = mc^2, where E is the energy released, m is the mass defect, and c is the speed of light. Substituting the given values, we have: E = (1.2 x 10^-5 kg) x (3.0 x 10^8 m/s)^2 E = (1.2 x 10^-5 kg) x (9.0 x 10^16 m^2/s^2) E = 1.08 x 10^12 J Therefore, the energy released in the nuclear fission process is 1.08 x 10^12 J. So the answer is (c) 1.08 x 10^12 J.

The pressure applied to an enclosed fluid to one end id transmitted equally throughout the fluid and to the container walls. This statement is

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The statement mentioned in the question is related to Pascal's principle. Pascal's principle states that the pressure applied to an enclosed fluid in a container is transmitted equally throughout the fluid and to the container walls. This principle is based on the fact that fluids are incompressible, which means that they cannot be compressed or squeezed into a smaller volume. Therefore, any pressure applied to one end of the fluid is transmitted equally to all parts of the fluid and to the walls of the container. This principle is used in many applications, including hydraulic systems, where a small force applied to one end of a piston is transmitted to a larger force at the other end, allowing heavy loads to be lifted with ease.

Which of the following concepts is a method of heat transfer that does not require a material medium?

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The correct answer is radiation. Radiation is a method of heat transfer that does not require a material medium. It involves the transfer of heat through electromagnetic waves, such as infrared radiation. Radiation can occur through a vacuum, which means that it can take place even in the absence of a medium or matter. Examples of radiation include the warmth you feel from the sun, the heat emitted by a fire, and the energy released by a light bulb.

Which of the following statements describes a body in a stable equilibrium correctly?

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The crackling noise produced by aluminum roofing sheets on a house during a hot sunny day is a result of

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The crackling noise produced by aluminum roofing sheets on a house during a hot sunny day is a result of the expansion of the sheets. The heat from the sun causes the metal to expand, and as a result, the sheets push against each other, making the crackling noise. This is because metal expands when heated and contracts when cooled. So during a hot day, the metal expands, and as it cools down in the evening, it contracts, which may also produce a similar noise.

In a school compound a girl walks 40km due east from the laboratory to the staff room to submit her report. Then she returns and walks 30m due north to her classroom. Determine the magnitude of her displacement from the10m laboratory

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Which of the following units is the S.I. unit of heat capacity?

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The S.I. unit of heat capacity is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius. Heat capacity is measured in Joules per Kelvin (J/K) or Joules per degree Celsius (J/°C). Therefore, the correct option is JK^-1, which stands for Joules per Kelvin.

An object is placed 20cm from a concave mirror of focal length 15cm. Calculate the linear magnification of the image formed

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The linear magnification of an image formed by a spherical mirror is given by the formula: magnification = height of image / height of object = -v/u where u is the object distance, v is the image distance and the negative sign indicates that the image is inverted. Given that the object is placed 20cm from a concave mirror of focal length 15cm, we can use the mirror formula: 1/f = 1/u + 1/v Rearranging this formula, we get: 1/v = 1/f - 1/u Substituting the given values, we get: 1/v = 1/15 - 1/20 1/v = (4 - 3)/60 1/v = 1/60 v = 60 cm Now, the magnification can be calculated as: magnification = -v/u = -60/20 = -3 Therefore, the linear magnification of the image formed is 3. Since the image is inverted, the sign of the magnification is negative. So, the correct answer is (d) 3.0.

What type of wave is emitted by a loud speaker?

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A loudspeaker emits a longitudinal wave. Sound waves are mechanical waves that travel through a medium by compressing and rarefying the particles of the medium. In a longitudinal wave, the displacement of the particles is parallel to the direction of wave propagation. When an electric current is applied to the speaker, it causes the speaker cone to vibrate back and forth, creating areas of compression and rarefaction in the surrounding air. These pressure waves then travel through the air to reach our ears, where they are detected as sound. Therefore, sound waves are examples of longitudinal waves.

A uniform bar AB is balanced on a knife-edge which is 60cm from B by a mass of 22g which hangs at C 10cm from A. Calculate the mass of the bar.

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Materials that can be stretched and still return to their original forms when the stresses are removed are said be

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Materials that can be stretched and still return to their original forms when the stresses are removed are said to be elastic. When a force is applied to an elastic material, it deforms in response to the force, but once the force is removed, the material returns to its original shape. This is due to the elastic material's ability to store the energy of deformation and then release it when the force is removed. Examples of elastic materials include rubber bands, springs, and certain types of metals.

Two angles of a pentagon are in the ratio 2:3. The others are 60^o each. Calculate the smaller of the two angles

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A wire of cross-sectional area 0.60mm² has a restivity of 7.2 x 10^-7 \(\Omega\). Calculate the length of wire that will have a resistance of 3\(\Omega\).

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The formula for calculating resistance is R = ρ(L/A), where R is the resistance of the wire, ρ is the resistivity of the wire material, L is the length of the wire, and A is the cross-sectional area of the wire. We are given the cross-sectional area and resistivity of the wire, as well as the desired resistance. We can rearrange the formula above to solve for L as follows: L = (RA)/ρ Substituting the given values, we get: L = (3 x 0.60 x 10^-6) / (7.2 x 10^-7) = 2.5 meters Therefore, the length of wire that will have a resistance of 3Ω is 2.5m. The correct option is (b) 2.50m.

Which of the following statements is correct? When capacitors of different values are connected in series

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When capacitors of different values are connected in series, the same charge flows through them. This is because the capacitors are connected in a series, so the same current flows through all of them. Since capacitors store charge, the same amount of charge must flow through each capacitor to maintain the same current. However, the voltage across each capacitor will be different, since the voltage drop across each capacitor will be proportional to its capacitance value. So, option A is correct.

The diagram given illustrates a wave form. Determine the speed of the wave

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The symbol illustrated above is that of a resistor?

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A battery of emf 24V is connected to three resistor P, Q and R as illustrated in the diagram. Determine the voltage across the resistor Q

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What must be connected between the points P and Q to establish a steady current through the incomplete circuit diagram given?

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To establish a steady current through the incomplete circuit diagram, a cell (battery) must be connected between the points P and Q. A cell provides the potential difference (voltage) required for the current to flow in the circuit. Without a cell, the circuit is incomplete, and no current will flow. Therefore, the correct answer is option C, cell.

An object is placed 15cm from a diverging lens of focal length 12cm. The image of the object formed by the lens in

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The resultant force in a couple is

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In a couple, two equal and opposite forces act on a body, but they are not in the same line. The resultant force of a couple is defined as the algebraic sum of the forces, which is zero because the forces are equal in magnitude and opposite in direction. However, the couple produces a turning effect or torque on the body, which is not zero, and depends on the magnitude of the forces and the distance between them. So the answer is (a) zero.

A body is projected with an initial velocity U at an angle O to the horizontal. The time taken by it to reach its maximum height is given by the expression

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When a projectile is projected with an initial velocity U at an angle O to the horizontal, it follows a parabolic path. The projectile reaches the maximum height at a certain point, then falls back to the ground. At the highest point, the vertical component of the velocity becomes zero. Let's assume that the time taken by the body to reach the maximum height is t. At the maximum height, the vertical component of the velocity becomes zero. Therefore, using the first equation of motion: v = u + gt where v = 0 and u = Usinθ 0 = Usinθ - gt gt = Usinθ t = Usinθ/g Therefore, the time taken by the body to reach its maximum height is given by the expression: t = Usinθ/g Thus, the correct option is: \(\frac{u \text{sin}\theta}{g}\)

The barometric reading at a place is 73.5m Hg. Calculate the pressure at a point 30m below the surface of water contained in a reservoir at the place. [g = ms^-2, density = 1.2 x 10⁴kg m^-3, density of water = 1.0 x 10³m^-3]

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Which of the following statements about a three-pin plug is/are correct. i. The brown wire is the live wire. ii. The fuse is connected to the live wire. iii. The earth wire is coloured blue

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The diagram given illustrates two charged particles W and X. The charges on W and x are respectively

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Which of the following radiations constitutes a stream of electrons?

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Cathode rays constitute a stream of electrons. Cathode rays are a stream of negatively charged particles (electrons) emitted from the negative electrode or cathode in a vacuum tube, also called a cathode ray tube. The electrons are accelerated by an electric field and focused into a beam that can be used for various applications such as in televisions and computer monitors. Therefore, is the correct answer.

Red light travels faster than blue light when both of them pass through a glass prism because the

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An object floats in a fluid when it displaces it's

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An object floats in a fluid when it displaces its weight of the fluid in which it floats. This is known as Archimedes' principle. The principle states that any object, wholly or partially immersed in a fluid, experiences an upward buoyant force equal in magnitude to the weight of the fluid displaced by the object. If the buoyant force is greater than or equal to the weight of the object, the object will float in the fluid.

A battery of emf 24V is connected to three resistor P, Q and R as illustrated in the given diagram. Determine the voltage across the resistor Q.

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Which of the following statements about mass and weight are correct? i. Weight is the force of gravity on a body. ii. The mass of a body is the quantity of matter in the body. iii. The weight of a body is greatest at the equator. iv. The mass of a body is greatest at the poles

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Which of the following units is derived?

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The derived units are those that can be obtained from the combination of two or more base units. Among the options given, N (Newton) is a derived unit because it is obtained from the combination of kg (kilogram), m (meter), and s (second) through the formula F=ma, where F is the force in N, m is the mass in kg, and a is the acceleration in m/s^2. On the other hand, kg (kilogram), m (meter), and K (Kelvin) are base units because they are independent and cannot be derived from any other unit.

The angle which the direction of the earth magnetic field makes with the horizontal at a palace is know as.

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The angle which the direction of the earth magnetic field makes with the horizontal at a place is known as the "angle of dip". This angle represents the inclination of the Earth's magnetic field lines with respect to the horizontal plane at a particular location. It is also known as the magnetic inclination or magnetic dip angle. The angle of dip varies at different locations on the Earth's surface, and it can be used to determine the position of the magnetic poles.

TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with a retort stand, boss head, clamp, stopwatch, slotted weights, hanger, grooved pulley, thread, measuring tape, and other necessary materials.

i. Measure and record the radius R of the pulley.

ii. Setup the apparatus as illustrated in the diagram above, such that the clamp is 1.5 m above the floor.

iii. Tie one end of the thread to the pulley.

iv. Tie the other end of the thread to the hanger.

v. Slot a mass m= 50 g on the hanger.

vi. Wind the thread around the groove of the pulley until the base of the hanger is at a height h = 1.4 m above the floor. Maintain this height h for every other value of m through out the experiment.

vii. Release the mass to unwind the thread.

viii. Determine and record the time t taken by the mass m to reach the floor.

ix. Evaluate t\(^{2}\)

x.  Also evaluate
a =\(\frac{2h}{t^{2}}\),T = \(\frac{m}{1000}\) (10 - a) and \(\propto\) = \(\frac{a}{R}\)

xi. Repeat the procedure for four other values of m = 70 g, 90 g, 110 g and 130 g

xii. Tabulate your readings.

xiii. Plot a graph with \(\propto\) on the vertical axis and T on the horizontal axis.

xiv. Determine the slope s, of the graph.

xv. Evaluate  I = \(\frac{R}{s}\).

xvi. State two precautions taken to obtain accurate results.

(b)i. Define centripetal force

ii. An object drops to the ground from a height of 2.0 m. Calculate the speed with which it strikes the ground. [g=10 ms\(^{-2}\)]

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You have been provided with a resistance box, a voltmeter, a key, a battery, and other necessary materials.

• Connect the circuit as shown in the diagram above.
• With the key K closed, read and record the voltmeter reading V\(_{0}\).
• Set the resistance R in the resistance box equal to I\(\Omega\).
•  Close the key, read and record the potential difference V on the voltmeter.
• EvaluateR\(^{-1}\) and V\(^{-1}\) .
• Repeat the procedure for five other values or R = 2\(\Omega\), 3\(\Omega\), 4\(\Omega\), 5\(\Omega\) and 6\(\Omega\).
• Tabulate your readings.
• Plot a graph with V\(^{-1}\) on the vertical axis and R on the horizontal axis.
• Determine the slope, s, of the graph and the intercept, C, on the vertical axis.
• Evaluate c\(^{-1}\)
• State two precautions taken to obtain accurate results.

(b)i. Define the potential difference between two points in an electric circuit.

ii. Explain why the emf of a cell is greater than the p.d. across the call when it is supplying Current through an external resistance.

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(a)(i) what is resonance?

(ii) State two eXwilples of resonance.

(iii) Differentiate between loudness and intensity of sound.

(b) When a ray is refracted through a rectangular glass prism, which of the following properties of the ray will change? Wavelength, frequency and speed.

(c)

(i) Copy the diagram above in your answer booklet.

(iii) On the copied diagram, sketch the pattern of the waves immediately after passing through the opening.

(d) A diverging lens of focal length 18.0 in is used to view a shark that is 90.0 in away from the lens. If the image formed is 1.0 m long, calculate the:

(i) image distance;

(ii) length of the shark.  

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(a) Define:(i) the coulomb; (ii) resistance.

(b) State the three effects of an electric current.

(c) State the standard international colour convention for the insulating material covering the following electrical wires in a three-pin plug: (i) live; (ii) neutral; (iii) earth.

(d)

A water melon of mass 5.0 kg is suspended on a uniform rod of mass 4.0 kg and 4.0 in long as illustrated in the diagram above. If the rod is in equilibrium by the action of the force between the charges +q and -q, calculate the:

(i) anti-clockwise moment;
(ii) value of q. [ g = 10 ms\(^{-2}\)]

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(a) What is doping in a semi conductor?

(b) Draw the symbol for OR gate.  

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 (a) Define nucleon number

(b) A radioactive isotope of Americium (Am —241) decays into a nucleus of Neptunium (Np — 237) and an alpha (\(\alpha\)) particle as shown in the nuclear equation below. \(^{241}_{95}Am\) \(\to\) \(^{237}_{c} + ^b_a \alpha\)

(i) State the number of neutrons in the nucleus of Americium — 241.

(ii) Determine the values of a,b and c.

(c)(i) Why are y-rays not deflected by electromagnetic field?

(ii) State two properties of gamma rays that make them suitable for sterilizing medical equipment.

(d) A sample of radioactive substance was found to be left with h of its initial count rate after 110 years. Calculate its decay constant.

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(a) (i) Define uniform acceleration.

(ii) Write an equation that relates linear velocity, angular velocity and radius
of path in circular motion.

(b) Two forces 30 N and 40 N act at right angles to each other. Determine by scale drawing, the magnitude and direction of the resultant force,.using a scale of 1 cm to 5 N.

(c) Explain why ships are usually refilled with sand and water after they have been emptied of their cargo.

(d) A crate of drinks of mass 20 kg is placed on a plane inclined at 30° to the horizontal. If the crate slides down with a constant speed, calculate the:

(i) co-efficient of kinetic friction;

(ii) magnitude of the frictional force acting on the crate. [ g = 10 ms\(^{-2}\)]

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A body is projected at an angle of 30° to the horizontal with a velocity of 150 ms\(^{-1.}\). Calculate the time it takes to reach the greatest height [Take g = 10 ms\(^2\) and neglect air resistance]

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(a) Write the de Broglie equation.

(b) Explain the significance of the equation.

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The circuit above consists of an a. c. voltage input, a diode, a resistor and a voltmeter.

(a) Identify the circuit.

(b) Draw the waveform for the output voltage.

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with a triangular glass prism, four optical pins, and other necessary materials.

• Place the triangular glass prism on a drawing paper and draw its outline UMR. Remove the prism.
• Measure and record the value of the angle at U.
• Draw a normal to the line UM at N. Also, draw another line TN to the normal such that \(\phi\)-60. Fix two pins at P\(_{1}\) and P\(_{2}\).
• Replace the prism and fix two other pains at P\(_{3}\), and P\(_{4}\), such that the pins appear to be in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\), when viewed from the side UR. Remove the prism.
• Join points P\(_{3}\), and P\(_{4}\), producing the line to meet TN produced at Z. Draw the normal XY.
• Measure and record the angle of emergence e and that of deviation d.
• Repeat the experiment with \(\phi\) = 55°, 50°, 40° and 35°.
• In each case, measure and record the Corresponding values of e and d.
• Tabulate your readings.
• Plot a graph with d on the vertical axis and e on the horizontal axis starting both axes from the origin (0.0) Join your points with a smooth curve.
• From your graph, obtain the minimum deviation d\(_{m}\) and the corresponding angle of emergence e\(_{m}\) . Hence, calculate the refractive index n of the prism using the formula:

n = \(\frac{sin (\frac{d_{m}+U}{2})}{sin{(\frac{u}{2})}}\)

• State two precautions taken to obtain accurate results. Attach your traces to your answer booklet.

(b)i. State the conditions necessary for total internal reflection of light to occur.

ii. The critical angle for a transparent substance is 39°. Calculate the refractive index of the substance.

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State three ways of increasing the rate of cooling of a cup of hot tea.

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