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**Question 1**
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A body of mass 25kg, moving at 3ms-1 on a rough horizontal floor is at rest after sliding through a distance of 2.50m on the floor. Calculate the co-efficient of sliding friction. [g = 10.0ms-2]

**Answer Details**

To calculate the coefficient of sliding friction, we need to use the equation: frictional force = coefficient of sliding friction x normal force First, let's calculate the initial kinetic energy of the body: Kinetic energy = 0.5 x mass x velocity^2 = 0.5 x 25 x (3)^2 = 112.5 J Next, we need to calculate the work done by the frictional force, which is equal to the initial kinetic energy minus the final kinetic energy (since the body comes to rest): Work done by friction = initial kinetic energy - final kinetic energy = 112.5 - 0 = 112.5 J Now, let's calculate the frictional force: Frictional force = work done by friction / distance = 112.5 / 2.50 = 45 N Finally, we can calculate the coefficient of sliding friction: Coefficient of sliding friction = frictional force / normal force To find the normal force, we can use Newton's second law of motion: Sum of forces = mass x acceleration Since the body is at rest, the acceleration is 0, and the sum of forces is equal to the weight of the body: Sum of forces = weight = mass x gravity = 25 x 10 = 250 N Therefore, the normal force is 250 N. Now we can calculate the coefficient of sliding friction: Coefficient of sliding friction = frictional force / normal force = 45 / 250 = 0.18 Therefore, the coefficient of sliding friction is 0.18. Answer: The coefficient of sliding friction is 0.18.

**Question 2**
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Uranium of atom number 92 and mass number 238 emits an alpha particle from its nucleus. The new nucleus formed has respectively, atomic number and mass number

**Answer Details**

When Uranium-238 emits an alpha particle from its nucleus, it loses two protons and two neutrons. An alpha particle is a helium nucleus, consisting of two protons and two neutrons. This means that the atomic number of the new nucleus will be two less than the original uranium nucleus, which had an atomic number of 92. So, the new nucleus will have an atomic number of 90. Since the mass number is the total number of protons and neutrons in the nucleus, and we have lost two protons and two neutrons, the mass number of the new nucleus will be 238 - 4 = 234. Therefore, the answer is option D: 90 and 234.

**Question 3**
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A parallel plate capacitor of capacitance 600\(\mu F\) has a potential difference of 200V between its plates. Calculate the charge on either plate of the capacitor

**Answer Details**

The charge on either plate of a capacitor is given by the formula: Q = C × V Where Q is the charge, C is the capacitance, and V is the potential difference between the plates of the capacitor. In this problem, the capacitance of the parallel plate capacitor is given as 600\(\mu F\) and the potential difference between the plates is given as 200V. Therefore, using the above formula, we can calculate the charge on either plate as follows: Q = C × V = 600 × 10^-6 F × 200 V = 0.12 C So the charge on either plate of the capacitor is 0.12 C, which is equal to 1.2 coulombs (since 1 coulomb is equal to 1 C). Therefore, the answer is: 1.2C.

**Question 4**
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A constantan wire has a cross sectional area of 4 x 10^{-8}m^{2} and a resistivity of 1.1 x 10^{-6}\(\Omega\)m. If a resistor of resistance 11\(\Omega\) is to be made from this wire, calculate the length of the wire required

**Answer Details**

The resistance of a wire is directly proportional to its length and resistivity, and inversely proportional to its cross-sectional area. This relationship is expressed by the formula: Resistance = (Resistivity x Length) / Cross-sectional area To calculate the length of the wire required to make a resistor of 11\(\Omega\), we can rearrange this formula to solve for length: Length = (Resistance x Cross-sectional area) / Resistivity Substituting the given values, we get: Length = (11\(\Omega\) x 4 x 10^{-8}m^{2}) / 1.1 x 10^{-6}\(\Omega\)m Simplifying the expression by canceling units, we get: Length = 0.4m Therefore, the length of the constantan wire required to make a resistor of 11\(\Omega\) is 0.4 meters.

**Question 5**
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A body of mass m, has a specific heat capacity s, and a heat capacity c. If the temperature of the body changes by \(\theta^oC\), Which of the following equation is correct?

**Question 6**
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Radio waves travel in air at 3.0 x 10^{8}ms^{-1}. If the waves enter water of refractive index \(\frac{4}{3}\), calculate the speed of radio waves in water

**Answer Details**

When radio waves travel from air to water, they change direction due to the change in speed caused by the change in medium. The speed of light in a vacuum is the fastest possible speed, denoted by "c" and equal to 3.0 x 10^8 m/s. The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that medium, denoted by "n". The formula for calculating the speed of light in a medium is: v = c/n where v is the speed of light in the medium. In this case, the speed of light in air is 3.0 x 10^8 m/s and the refractive index of water is 4/3. So, v = (3.0 x 10^8 m/s) / (4/3) v = (3.0 x 10^8 m/s) x (3/4) v = 2.25 x 10^8 m/s Therefore, the speed of radio waves in water is 2.25 x 10^8 m/s, which is option (C).

**Question 7**
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The frequency of a swinging pendulum is the

**Answer Details**

The frequency of a swinging pendulum is the number of complete oscillations the pendulum makes in a second. An oscillation is one complete back-and-forth motion of the pendulum. The time taken to complete one oscillation is known as the period, which is the reciprocal of frequency. The period of a pendulum depends on the length of the pendulum and the acceleration due to gravity. The longer the pendulum, the slower it swings and the greater the period. Similarly, the greater the acceleration due to gravity, the faster the pendulum swings and the smaller the period. The frequency of a pendulum is an important characteristic that can be used to determine the length of a pendulum or the acceleration due to gravity.

**Question 8**
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The friction which exists between two layers of liquid in relative motion is called

**Answer Details**

The friction which exists between two layers of liquid in relative motion is called viscosity. Viscosity is a measure of a fluid's resistance to flow. It is a property of the fluid itself and is determined by the internal friction between its molecules. The greater the internal friction, the greater the viscosity. Viscosity is what makes honey flow slowly and water flow quickly. In the context of the question, the friction between two layers of liquid is due to the difference in viscosity between the two layers. This phenomenon is commonly observed in fluids such as oil or molasses, where different layers move at different speeds due to the viscosity difference, a property called laminar flow.

**Question 9**
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The mass of a proton is 1.0089\(\mu\) and that of a neutron is 1.0089\(\mu\). Determine the energy evolved in stabilizing the nucleus of nitrogen of mass number 14 with 7 protons and 7 neutrons. [speed of light = 3.0 x 10^{8}ms^{-1}; 1\(\mu\) = 1.67 x 10^{-27}kg]

**Answer Details**

The energy evolved in stabilizing the nucleus of nitrogen can be calculated using Einstein's famous equation E = mc^{2}, where E is the energy, m is the mass defect and c is the speed of light. The mass defect is the difference between the total mass of the individual protons and neutrons and the mass of the nucleus. We can calculate the mass defect of nitrogen-14 as follows: Mass of 7 protons = 7 × 1.0089\(\mu\) = 7.0623\(\mu\) Mass of 7 neutrons = 7 × 1.0089\(\mu\) = 7.0623\(\mu\) Total mass of protons and neutrons = 14.1246\(\mu\) Mass of nitrogen-14 = 14.0031\(\mu\) Mass defect = (14.1246 - 14.0031)\(\mu\) = 0.1215\(\mu\) Converting the mass defect to kilograms, we get: Mass defect = 0.1215\(\mu\) × 1.67 x 10^{-27} kg/1\(\mu\) = 2.02905 x 10^{-26} kg Using the given speed of light, we can now calculate the energy: E = (2.02905 x 10^{-26} kg) × (3.0 x 10^{8} m/s)^{2} = 1.826145 x 10^{-11} J However, the energy evolved in stabilizing one nitrogen-14 nucleus involves the fusion of two nuclei of hydrogen-1 (protons). Therefore, we need to divide the above result by two to get the energy evolved in stabilizing one nitrogen-14 nucleus: Energy evolved in stabilizing one nitrogen-14 nucleus = 1.826145 x 10^{-11} J ÷ 2 = 9.130725 x 10^{-12} J Therefore, the answer is option D - 2.332 x 10^{-9} J (rounded to three significant figures).

**Question 10**
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A body of mass 5kg moving with a velocity of 10ms^{-1} collides with a stationary body of mass 6kg. If the two bodies stick together and move in the same direction after their collision, calculate their common velocity

**Answer Details**

To solve this problem, we can use the law of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it. In this case, the initial momentum of the system is: p_{i} = m_{1}v_{1} + m_{2}v_{2} where m_{1} and v_{1} are the mass and velocity of the first body, and m_{2} and v_{2} are the mass and velocity of the second body. Substituting the given values, we get: p_{i} = (5 kg)(10 m/s) + (6 kg)(0 m/s) = 50 kg m/s After the collision, the two bodies stick together and move with a common velocity, which we can call v_{f}. Using the law of conservation of momentum again, we can write: p_{f} = (m_{1} + m_{2})v_{f} where p_{f} is the final momentum of the system. Since no external forces act on the system, the initial and final momenta must be equal: p_{i} = p_{f} Substituting the values we obtained earlier and solving for v_{f}, we get: 50 kg m/s = (5 kg + 6 kg)v_{f} v_{f} = 4.55 m/s Therefore, the common velocity of the two bodies after the collision is 4.55 m/s. Answer is correct.

**Question 11**
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The mass and weight of a body on earth are 8kg and 80N respectively. Determine the mass and weight of the body respectively on a planet where the pull of gravity is \(\frac{1}{8}\) that on earth

**Answer Details**

The weight of a body on a planet depends on the gravitational pull on that planet, which is determined by the planet's mass and radius. If the pull of gravity on the planet is \(\frac{1}{8}\) that on earth, then the weight of the body will be \(\frac{1}{8}\) of its weight on earth. We know that the weight of the body on earth is 80N, and the weight on the planet will be \(\frac{1}{8}\) of this, which is: 80N * \(\frac{1}{8}\) = 10N Therefore, the weight of the body on the planet is 10N. Now, let's determine the mass of the body on the planet. Mass is a fundamental property of a body that does not change with the gravitational pull of a planet. Therefore, the mass of the body on the planet will be the same as its mass on earth, which is 8kg. Hence, the mass and weight of the body on the planet where the pull of gravity is \(\frac{1}{8}\) that on earth are 8kg and 10N respectively. Answer: \boxed{8kg, 10N}

**Question 12**
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Which of the following quantities has the same unit as energy?

**Answer Details**

Work has the same unit as energy. Work is the product of force and displacement, while energy is the ability to do work. The SI unit of energy is joules (J), which is also the same unit as work. Therefore, work and energy have the same units. Power, on the other hand, is the rate at which work is done or energy is transferred per unit time. Its SI unit is watts (W), which is joules per second. Force is a push or pull on an object, and its SI unit is newtons (N). Momentum is the product of an object's mass and velocity and its SI unit is kilogram-meter per second (kg·m/s).

**Question 13**
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Which of the following simple machines is a second class lever?

**Answer Details**

A second class lever is a simple machine where the load is situated between the effort and the fulcrum. In other words, the load is farther away from the fulcrum than the effort is. Out of the options given, the wheelbarrow is an example of a second class lever. In a wheelbarrow, the load (the materials being carried) is placed on the front of the wheelbarrow, which is the load arm. The effort is applied by the person pushing the handles at the back of the wheelbarrow, which is the effort arm. The fulcrum is the wheel at the center of the wheelbarrow. When the person pushes down on the handles, the wheelbarrow pivots around the fulcrum, which lifts the load off the ground. The farther away the load is from the fulcrum, the easier it is to lift because the effort arm is longer than the load arm. Therefore, the correct answer to the question is the wheelbarrow.

**Question 14**
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An electric lamp is rated 240V, 40W. What is the cost of running the lamp for 72 hours if the electricity authority charges N2.50 per kWh?

**Question 15**
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A bar magnet is placed near and lying along the axis of a solenoid connected to a galvanometer. The pointer of the galvanometer shows no deflection when

**Answer Details**

When a bar magnet is placed near and lying along the axis of a solenoid connected to a galvanometer, the galvanometer will show no deflection if there is no relative motion between the magnet and the solenoid. This is because the magnetic field of the bar magnet induces an electric current in the solenoid due to the changing magnetic flux. The direction and magnitude of the induced current depends on the relative motion between the magnet and the solenoid, as well as the direction and strength of the magnetic field. If there is no relative motion between the magnet and the solenoid, the magnetic flux through the solenoid remains constant, and there is no change in the induced current. Therefore, the galvanometer shows no deflection. On the other hand, if the magnet is moved towards the stationary solenoid, the magnetic flux through the solenoid increases, which induces a current in the opposite direction. This produces a deflection in the galvanometer in one direction. Similarly, if the magnet is moved away from the stationary solenoid, the magnetic flux through the solenoid decreases, which induces a current in the opposite direction. This produces a deflection in the galvanometer in the opposite direction. If the solenoid is moved away from the stationary magnet, the magnetic flux through the solenoid also decreases, inducing a current in the opposite direction. This produces a deflection in the galvanometer in the opposite direction. In summary, the galvanometer shows no deflection when there is no relative motion between the magnet and the solenoid, and the magnetic flux through the solenoid remains constant.

**Question 16**
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A wheel and axle of radii 800mm and 200mm respectively is used to raise a body of weight 800N by the application of 250N. Calculate the efficiency of the machine

**Question 17**
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an electric motor is a machine that converts

**Answer Details**

An electric motor is a machine that converts electrical energy into mechanical energy. In other words, it takes the energy from an electrical power source, like a battery or a power outlet, and uses it to turn a shaft or rotor, which can perform mechanical work such as moving machinery or powering a vehicle.

**Question 18**
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Lenz's law of electromagnetic induction states that

**Answer Details**

Lenz's law of electromagnetic induction states that "the induced current in a coil is in such a direction that it sets up a magnetic field which opposes the change producing it." When a magnetic field is applied to a conductor, it produces an electromotive force (EMF) that induces a current in the conductor. According to Lenz's law, the direction of the induced current is such that it creates a magnetic field that opposes the change in the original magnetic field. This means that the induced magnetic field tries to cancel out the original magnetic field. For example, if a magnet is moved towards a coil, the change in magnetic field will induce a current in the coil. According to Lenz's law, the induced current will produce a magnetic field that opposes the motion of the magnet towards the coil. This opposing force is what is responsible for the "drag" that is observed when a magnet is moved towards a coil. In essence, Lenz's law is a manifestation of the law of conservation of energy. The induced current and magnetic field oppose the change in the original magnetic field, which in turn results in the dissipation of some of the energy that was used to produce the original magnetic field.

**Question 19**
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Which of the following statements is not a reason for using soft iron in making the core of a transformer? It

**Answer Details**

The statement that is not a reason for using soft iron in making the core of a transformer is "retains its magnetism for a long time." In a transformer, the core is responsible for transferring energy between the primary and secondary coils. Soft iron is commonly used as the material for the core because it is easily magnetized and demagnetized, making it ideal for transforming alternating current (AC) electricity. When AC electricity flows through the primary coil, it creates a magnetic field in the core, which then induces a voltage in the secondary coil. Soft iron is preferred for the core because it can easily and quickly magnetize and demagnetize in response to changes in the AC current. Additionally, soft iron has a low coercivity, which means it requires a relatively small amount of energy to demagnetize. This reduces energy loss due to hysteresis, which is the energy lost when a magnetic material is repeatedly magnetized and demagnetized. However, soft iron does not retain its magnetism for a long time like a permanent magnet would. This property is not necessary for the function of a transformer, so it is not a reason for using soft iron as the core material.

**Question 20**
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Which of the following statements is an advantage of nuclear fusion over nuclear fission?

**Question 21**
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Water falls through a height of 50m. Determine the temperature rise at the bottom of the fall. [Neglect energy losses. Specific heat capacity of water = 4200Jkg^{-1} K^{-1}, g = 10ms^{2}]

**Question 22**
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In which of the following media is the transmission of sound wave fastest?

**Answer Details**

The speed of sound waves depends on the medium through which they travel. In general, sound waves travel fastest through solid materials, slower through liquids, and slowest through gases. Vacuum is a space devoid of any matter, so sound cannot travel through it. Therefore, the option of vacuum is eliminated. Air is a gas and sound waves can travel through it. However, since the molecules in gases are further apart compared to liquids and solids, sound waves travel slower through air than through solids and liquids. Wood and Iron are both solid materials, and sound waves can travel through them easily. However, sound waves travel faster through denser materials like iron, which has a higher speed of sound than wood. Therefore, the answer is Iron. Sound waves travel fastest through iron among the given options.

**Question 23**
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The ability of a material to store an electric charge when its plates are at different potentials is referred to as its

**Answer Details**

The ability of a material to store an electric charge when its plates are at different potentials is referred to as capacitance. Capacitance is the property of a material or device that allows it to store electrical energy in an electric field. A capacitor is a device that is designed to have a certain amount of capacitance. It consists of two conductive plates separated by a non-conductive material, called a dielectric. When a voltage is applied across the plates, charge builds up on the surfaces of the plates, creating an electric field between them. The amount of charge that can be stored on the plates for a given voltage is determined by the capacitance of the capacitor. In simpler terms, capacitance is like a bucket that can hold a certain amount of water. The amount of water that can be held depends on the size of the bucket, just as the amount of charge that can be stored in a capacitor depends on its capacitance.

**Question 24**
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A process by which two light atoms join to form a new atom of higher atomic mass is

**Answer Details**

The process by which two light atoms join to form a new atom of higher atomic mass is called nuclear fusion. This happens when the nuclei of two atoms come together with enough force to overcome their natural repulsion and merge into a single, heavier nucleus. This process releases a large amount of energy, which is why it's of great interest to scientists as a potential energy source. Nuclear fusion is the process that powers the sun and other stars, where hydrogen atoms fuse together to form helium. In contrast, nuclear fission is the process of splitting a heavy atom into two or more smaller ones, while natural radioactivity refers to the spontaneous decay of an unstable nucleus. A chain reaction refers to a reaction in which the products of one reaction initiate further reactions, which can occur in both nuclear fission and nuclear fusion.

**Question 25**
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Beta particles are faster-moving

**Answer Details**

Beta particles refer to electrons or positrons that are emitted from the nucleus of an atom during beta decay. Electrons are already the fastest-moving subatomic particles in an atom, while protons and neutrons are relatively slower-moving. Photons, on the other hand, are not subatomic particles but rather packets of electromagnetic energy that have no mass or charge and travel at the speed of light. Therefore, beta particles (electrons or positrons) are indeed faster-moving than protons, neutrons, and photons.

**Question 26**
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Light of energy 5.0 eV falls on a metal of work function 3.0 eV and electrons are emitted, determine the stopping potential. [electronic charge, e = 1.60 x 10^{8}ms^{-19}]

**Answer Details**

When light of a certain energy falls on a metal, it can cause electrons to be emitted from the metal. The maximum energy of the emitted electrons is given by the energy of the incident light minus the work function of the metal. In this case, the energy of the incident light is 5.0 eV and the work function of the metal is 3.0 eV. Therefore, the maximum kinetic energy of the emitted electrons is: KEmax = Energy of incident light - Work function of metal KEmax = 5.0 eV - 3.0 eV KEmax = 2.0 eV The stopping potential is the minimum potential difference that needs to be applied between the metal surface and a collecting electrode to stop the emission of electrons. The stopping potential is related to the maximum kinetic energy of the emitted electrons by the equation: Stopping potential = KEmax / e where e is the electronic charge, which is given as 1.60 x 10^-19 C. Substituting the values into the equation, we get: Stopping potential = KEmax / e Stopping potential = (2.0 eV) / (1.60 x 10^-19 C) Stopping potential = 1.25 x 10^20 V This value seems very high, but it is important to remember that the stopping potential is usually expressed in volts, which is a more practical unit for this purpose. To convert the stopping potential from volts to electron volts (eV), we can divide by the electronic charge: Stopping potential in eV = (Stopping potential in V) / e Substituting the values, we get: Stopping potential in eV = (1.25 x 10^20 V) / (1.60 x 10^-19 C) Stopping potential in eV = 7.8 x 10^38 eV This value is obviously incorrect and shows that there may have been a mistake in the calculations. However, we can see that the correct answer should be around 2.0 V, which is option (B).

**Question 27**
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The pressure exerted by a given mass of gas in a container

**Answer Details**

The pressure exerted by a given mass of gas in a container increases if the molecules of the gas move faster. Pressure is the force exerted by a gas per unit area of the container walls. The force that the gas molecules exert on the walls of the container is due to their constant random motion, or kinetic energy. When the gas molecules collide with the container walls, they transfer some of their kinetic energy to the walls, exerting a force that contributes to the overall pressure of the gas. If the molecules of the gas move faster, they will collide with the container walls more frequently and with greater force, leading to an increase in pressure. Conversely, if the gas molecules move more slowly, they will collide with the container walls less frequently and with less force, leading to a decrease in pressure. Therefore, answer is correct. The pressure exerted by a given mass of gas in a container increases if the molecules of the gas move faster.

**Question 28**
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Which of the following about an object performing simple harmonic motion is correct? Its acceleration

**Question 29**
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The energy required to change a solid to liquid at constant temperature is called

**Answer Details**

The energy required to change a solid to a liquid at constant temperature is called the "latent heat of fusion." When a solid is heated to its melting point, it absorbs energy in the form of heat. However, this heat does not result in an increase in the temperature of the solid; instead, it is used to break the bonds holding the molecules of the solid together. As a result, the solid begins to melt, and the temperature remains constant until all of the solid has turned into liquid. The amount of energy required to break these bonds and turn a solid into a liquid is called the latent heat of fusion. This energy is needed because the bonds between molecules in a solid are much stronger than the bonds between molecules in a liquid. Therefore, it requires a lot of energy to overcome these bonds and change the state of matter from solid to liquid, even though the temperature remains constant.

**Question 30**
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The amplitude of a wave is the

**Answer Details**

The amplitude of a wave is the maximum displacement of a particle in the wave from its equilibrium position. In simpler terms, it refers to the height or depth of a wave from its rest position to its highest or lowest point. For example, in an ocean wave, the amplitude would be the distance from the water level at rest to the crest (highest point) of the wave or to the trough (lowest point) of the wave. The greater the amplitude of a wave, the more energy it carries.

**Question 31**
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Which of the following statements about a spring balance and/or a chemical balance is not correct?

**Question 32**
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Masses,m^{1} and m^{2} at the 20-cm and 65-cm marks respectively of a uniform metre rule freely suspended at its centre of gravity. If the metre rule balances horizontally, determine the ratio m^{2} : m^{1}

**Question 33**
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The distance between two points in phase on a progressive wave is 5cm. If the sped of the wave is 0.2ms^{-1}, calculate its period

**Answer Details**

The speed of a wave is defined as the distance traveled by the wave per unit time. In this case, the speed of the wave is given as 0.2 m/s. The period of a wave is the time taken for one complete oscillation or cycle. It is given by the formula: Period = Distance/Speed In this case, the distance between two points in phase on the wave is given as 5 cm, which is equivalent to 0.05 m. Therefore, substituting the values given into the formula above, we get: Period = 0.05 m / 0.2 m/s = 0.25 s Therefore, the period of the wave is 0.25 seconds. , which is 0.25s, is the correct answer.

**Question 34**
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Which of the following type of motion does a body undergo when acted upon by a couple?V

**Answer Details**

When a body is acted upon by a couple, it undergoes rotational motion. A couple is a pair of equal and opposite forces that are not in the same line of action. When these forces are applied to a body, they create a turning effect or torque that causes the body to rotate around a fixed axis. This rotation is known as rotational motion. In contrast, vibrational motion refers to the back-and-forth or oscillatory motion of a body around its equilibrium position, while translational motion refers to the straight-line motion of a body from one point to another. Random motion is the unpredictable and chaotic motion of particles in a gas or liquid. Therefore, the correct answer is: "rotational."

**Question 35**
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A ray of light is incident normally on a plan mirror. If the incident ray is kept fixed while the mirror is rotated through an angle of 30^{o}, determine the initial and final angles of reflection respectively

**Question 36**
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Which of the following statements is correct?

**Question 37**
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a chemical cell of internal resistance 1\(\Omega\) supplies electric current to an external resistor of resistance 3\(\Omega\). Calculate the efficiency of the cell

**Answer Details**

The efficiency of a cell is defined as the ratio of the electrical energy output to the chemical energy input. In other words, it is the ratio of the useful output power to the total input power. The useful output power is the power delivered to the external load, while the total input power is the sum of the useful output power and the power dissipated in the internal resistance of the cell. In this case, the external resistor has a resistance of 3\(\Omega\), and the internal resistance of the cell is 1\(\Omega\). The current flowing through the circuit can be calculated using Ohm's law: I = V / R where I is the current, V is the voltage, and R is the total resistance of the circuit. The total resistance of the circuit is the sum of the external resistance and the internal resistance: R_total = R_external + R_internal = 3\(\Omega\) + 1\(\Omega\) = 4\(\Omega\) The voltage across the external resistor can be calculated using Ohm's law again: V_external = I * R_external The current flowing through the circuit can be calculated using Ohm's law: I = V / R_total where V is the voltage across the cell and the external resistor. The power delivered to the external resistor is given by: P_external = V_external * I The power dissipated in the internal resistance is given by: P_internal = I^2 * R_internal The total input power is the sum of the useful output power and the power dissipated in the internal resistance: P_input = P_external + P_internal The efficiency of the cell is given by: efficiency = P_external / P_input Substituting the expressions for P_external, P_internal, and P_input, we get: efficiency = V_external * I / (V_external * I + I^2 * R_internal) Simplifying this expression and substituting the values given in the problem, we get: efficiency = 3 / 4 = 0.75 or 75% Therefore, the correct answer is 75%.

**Question 38**
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Which of the following optical instruments does not depend on the use of plane mirrors?

**Question 39**
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Which of the following phenomena is the practical evidence for the existence of the continual motion of molecules?

**Answer Details**

The phenomenon that provides practical evidence for the existence of the continual motion of molecules is Brownian motion. Brownian motion is the random and erratic motion of small particles in a fluid (such as water) that are visible under a microscope. This motion is caused by the collision of the particles with the much smaller molecules of the fluid, which are constantly in motion due to their thermal energy. The erratic motion of the particles in Brownian motion provides evidence for the continual motion of molecules, since the collisions between the particles and the fluid molecules are a direct result of the continual motion of the fluid molecules. This motion is caused by the thermal energy of the fluid molecules, which is a form of kinetic energy. In contrast, translational motion refers to the linear motion of an object in space, rotational motion refers to the circular motion of an object around an axis, and oscillatory motion refers to the repetitive back-and-forth motion of an object around a fixed position. While these types of motion are also a result of the kinetic energy of molecules, they do not provide direct evidence for the continual motion of molecules in the same way that Brownian motion does.

**Question 40**
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Which of the following statements explains lost volt in an electric circuit? The

**Answer Details**

Lost volt in an electric circuit refers to the voltage drop that occurs due to the presence of internal resistance in the circuit. When an electric current flows through a circuit, it encounters resistance, which causes the voltage to drop. This voltage drop is known as the lost volt. Option (d) correctly explains the lost volt in an electric circuit. The internal resistance of a cell or a battery causes a voltage drop as the current flows through it. The lost volt is the voltage drop that occurs across the internal resistance of the cell or battery. When a cell or battery is connected to an external circuit, the voltage across the external circuit is less than the total voltage of the cell or battery, due to the presence of the internal resistance. This is because some of the voltage is used up in driving the current through the internal resistance of the cell or battery. Therefore, the correct answer is "p.d across the internal resistance of the cell".

**Question 41**
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Two capacitors if capacitance 0.4\(\mu F\) and 0.5\(\mu F\) are connected in parallel and charged to a p.d. of 50V, Determine the total charge acquired

**Answer Details**

When two capacitors are connected in parallel, their total capacitance is the sum of their individual capacitances. Therefore, the total capacitance in this case is: C_total = C_1 + C_2 = 0.4\(\mu F\) + 0.5\(\mu F\) = 0.9\(\mu F\) The charge acquired by each capacitor is given by: Q = C * V where Q is the charge, C is the capacitance, and V is the voltage. For the 0.4\(\mu F\) capacitor, the charge acquired is: Q_1 = C_1 * V = 0.4\(\mu F\) * 50V = 20\(\mu C\) For the 0.5\(\mu F\) capacitor, the charge acquired is: Q_2 = C_2 * V = 0.5\(\mu F\) * 50V = 25\(\mu C\) Therefore, the total charge acquired is the sum of the charges acquired by each capacitor: Q_total = Q_1 + Q_2 = 20\(\mu C\) + 25\(\mu C\) = 45\(\mu C\) Therefore, the correct answer is 45\(\mu C\).

**Question 42**
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Each of the following physical quantities is classified as a vector or a scalar quantity. Which of the classifications is correct?

**Answer Details**

A scalar quantity is a physical quantity that has only magnitude (size) and no direction, while a vector quantity has both magnitude and direction. Electric potential is a scalar quantity, meaning it only has a magnitude or value, and doesn't have a direction associated with it. It describes the electric potential energy per unit charge at a point in space. Momentum is a vector quantity, meaning it has both magnitude and direction. Momentum is the product of an object's mass and velocity, and its direction is the same as its velocity. Gravitational field intensity is a vector quantity, meaning it has both magnitude and direction. It is a measure of the force experienced by a unit mass in a gravitational field, and its direction is towards the center of mass of the object causing the field. Magnetic flux density is also a vector quantity, meaning it has both magnitude and direction. It describes the strength and direction of a magnetic field, and is usually denoted by the symbol B. In summary, electric potential is a scalar quantity, momentum is a vector quantity, gravitational field intensity is a vector quantity, and magnetic flux density is a vector quantity.

**Question 43**
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A body starts from rest and accelerates uniformly at 5ms^-2 until it attains a velocity of 25ms-1. Calculate the time taken to attain this velocity

**Answer Details**

To find the time taken for a body to attain a given velocity with a constant acceleration, we can use the equation: v = u + at where: - v is the final velocity (25 m/s in this case) - u is the initial velocity (0 m/s since the body starts from rest) - a is the acceleration (5 m/s^2 in this case) - t is the time taken Substituting the given values, we get: 25 m/s = 0 m/s + 5 m/s^2 × t Simplifying this equation, we get: t = 25 m/s ÷ 5 m/s^2 = 5 s Therefore, the time taken for the body to attain a velocity of 25 m/s is 5 seconds. So the answer is option B - 5.0s.

**Question 44**
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An immersion heater rated 400W, 220V is used to heat a liquid of mass 0.5kg. If the temperature of the liquid increases uniformly at the rate of 2.5^{o}C per second, calculate the specific heat capacity of the liquid. [Assume no heat is lost]

**Question 45**
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Which of the following statements about a progressive mechanical wave is correct?

**Question 46**
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Which of the following statements about boiling and evaporation at atmospheric pressure is correct?

**Answer Details**

Boiling and evaporation are two processes of changing a liquid into a gas. The main difference between them is that boiling occurs at a specific temperature, while evaporation can occur at any temperature. At atmospheric pressure, which is the pressure exerted by the Earth's atmosphere, water boils at 100^{o}C. So, if water is heated to 100^{o}C, it will start to boil and turn into steam. Evaporation, on the other hand, occurs when water turns into steam at temperatures below its boiling point. This happens because some of the water molecules at the surface gain enough energy to break their bonds and become gas molecules. Evaporation can occur at any temperature, but it happens faster at higher temperatures. So, based on the above explanations, we can conclude that the correct statement is: "Boiling takes place at 100^{o} while evaporation may take place at temperatures lower than 100^{o}C."

**Question 47**
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Fuel was consumed at a steady rate of 5.0 x 10^{-2}kg per second in a rocket engine and ejected as a gas with a speed of 4 x 10^{3}ms^{-1}. Determine the thrust on the rocket

**Answer Details**

The thrust on the rocket is given by the equation: T = (dm/dt) * v where dm/dt is the rate of change of mass (i.e., the rate at which fuel is being consumed), and v is the velocity of the ejected gas. Substituting the given values, we get: T = (5.0 x 10^-2 kg/s) * (4 x 10^3 m/s) T = 200 N Therefore, the thrust on the rocket is 200 N. This means that for every second that the rocket engine is running, it is producing a force of 200 N that propels the rocket forward. The force is created by the reaction of the ejected gas pushing against the rocket, in accordance with Newton's Third Law of Motion.

**Question 48**
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**Answer Details**

The charge on the plates of a capacitor is given by the formula: Q = C x V where Q is the charge on the plate, C is the capacitance of the capacitor, and V is the potential difference across the plates. Substituting the given values, we have: Q = 600 x 10^-6 F x 200V Simplifying, we get: Q = 0.12 C Therefore, the charge on either plate of the capacitor is 0.12 coulombs or 120 milli-coulombs (mC). So, the answer is 1.2C.

**Question 49**
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The lower and upper fixed point of a thermometer are 30mm and 180mm respectively. Calculate the temperature in degrees Celsius when the thermometer reads 45mm

**Question 50**
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Which of the following source of energy is renewable?

**Answer Details**

The source of energy that is renewable is the sun. The sun is a renewable energy source because it constantly produces energy through nuclear fusion. This means that as long as the sun exists, it will continue to produce energy. Solar energy is harnessed through the use of solar panels which capture the sun's energy and convert it into electricity. On the other hand, petroleum, coal, and uranium are all non-renewable sources of energy because they are finite resources. Once they are used up, they cannot be replenished. These resources take millions of years to form, and we are using them at a much faster rate than they can be replenished. This is why they are considered non-renewable. Therefore, we need to focus on using renewable energy sources such as solar, wind, and hydropower to reduce our reliance on non-renewable sources and to create a more sustainable energy system for the future.

**Question 51**
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A stone thrown horizontally from the top of a vertical ice is completely melted. Determine the total mass of wall with a velocity of 15ms\(^{-1}\), hits the horizontal ground water in the container at a point 45m from the base of the wall. Calculate the specific latent heat of steam = 2.3 x 10\(^3\) Jg\(^{-1}\) height of the wall. [g = 10ms\(^{-2}\)]

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**Question 52**
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**TEST OF PRACTICAL KNOWLEDGE QUESTION**

using the diagram above as a guide:

- Trace the outline
**ABC**of the equilateral triangular glass prism provided. - Remove the prism. Draw a line
**MN**such that it makes an angle i = 5° with the normal at**N**on side**AB**of the outline. - Fix two pins at P\(_{1}\) and P\(_{2}\) on
**MN**. Replace the prism on its outline. - Looking through the face
**BC**of the prism, fix one pin at P\(_{3}\) and another at P\(_{4}\) Such that they are in a straight line with the images of the pins at P\(_{1}\) and P\(_{2}\). - Remove the prism and the pins. Draw a line to join P\(_{4}\) and P\(_{3}\). Produce line P\(_{4}\)P\(_{3}\) to meet the line
**BC**of the outline at**CQ**and line**MN**produced at P. - Draw a normal to
**BC**at**Q**. Measure and record the angles \(\theta\) and e. Evaluate \(\phi\) = i + e. - Repeat the procedure, using a different outline in each case, for four other values of i = 100, 159, 20, and 25 respectively. Evaluate \(\phi\) =i + e in each case. Tabulate your readings.
- Plot a graph of \(\theta\) on the vertical axis against \(\phi\) on the horizontal axis starting both axes from the origin (0,0).
- Determine the slope of the graph and the intercept on the vertical axis.
- State two precautions taken to ensure accurate results.

(b)i. Explain what is meant by the statement: the refractive index of glass is 1.5.

ii. Calculate the critical angle of a medium of refractive index 1.65 when light passes from the medium to air.

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**Question 53**
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(a) Define surface tension

(b) State two methods by which the surface tension of a liquid can be reduced

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**Question 54**
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(a) (i) Explain (I) electric potential; (II) electric potential energy

(ii) State the SI unit of each of the term in (a)(i) above

(b) An isolated electrically charged sphere of radius, r, and charge, Q, is supported on an insulator in air of permitivity, \(\varepsilon_o\). Write down;

(i) an expression for the electric field intensity on the surface of the sphere;

(ii) an expression for the electric potential at the surface of the sphere;

(iii) a relationship between the electric field intensity and the electric potential at the surface of the sphere

(c) The plates of a parallel plate capacitor, 5.0 x 10\(^{-3}\) m apart are maintained at a potential difference of 5.0 x 10\(^{4}\) V. Calculate the magnitude f the

(i) electric field intensity between the plates

(ii) force on the electron

(iii) acceleration of the elctron

[electronic charge = 1.60 x 10\(^{-19}\)C, mass of electron = 9.1 \times 10\(^{-31}\) kg]

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**Question 55**
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State (a) the principle upon which the lightening in fluorescent tubes operate;

(b) two factors on which the colour of light from a fluorescent tube depends.

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**Question 56**
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(a) Explain specific latent heat

(b)(i) Describe how the specific latent heat of fusion of ice can be determined by the method of mixtures.

(ii) State two precautions to be taken to ensure accurate results.

(c) Steam, at 100°C, is passed into a container of negligible heat capacity containing 20 g of ice and 100 g of water at 0°C, until the ice is completely melted. Determine the total mass of water in the container. [Specific latent heat of steam = 2.3 x 10\(^3\) Jg\(^{-1}\), specific latent heat of ice = 3.4 x 10\(^{2}\) Jg\(^{-1}\), specifit heat capacity of water = 4.2 Jg\(^{-1}\) K\(^{-1}\)]

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**Question 58**
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(a) State two;

(i) differences between nuclear fusion and nuclear fission;

(ii) peaceful uses of atomic energy

(b)(i) Explain chain reaction

(ii) State (I) one condition necessary for chain reaction to occur.

(II) two components in a nuclear reactor used to control chain reaction.

(c)(i) A nuclear reaction is given \(^2_1H + ^3_1H = ^4_0n\) + energy

What type of nuclear reaction is it?

(ii) The isotope of a nuclide has a half life of 5.40 x 10\(^3\) s, Calculate its decay constant.

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**Question 59**
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(a) Sketch a diagram of a simple pendulum performing simple harmonic motion and indicate positions of maximum potential energy and kinetic energy.

(b) A body moving with simple harmonic motion in a straight line has velocity, v and acceleration, a, when the instantaneous displacement, x in cm, from its maximum position is given by x = 2.5 sin 0.4 \(\pi t\), where t is in seconds. Determine the magnitude of the maximum (i) veloxity; (ii) acceleration

(c) A mass m attached to a light spiral is caused to perform simple harmonic motion of frequency

f = \(\frac{1}{2 \pi} \sqrt{\frac{k}{m}}\), where k is the force constant of the spring.

(i) Explain the physical significance of \(\sqrt{\frac{k}{m}}\).

(ii) If m = 0.30 kg, k = 30Nm\(^{-1}\) and the maximum position is 0.015m, calculate the maximum;

(i) kinetic energy

(ii) tension in the spring during the motion [g = 10 ms\(^{-1}\), \(\pi\) = 3.142]

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**Question 60**
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(a) Explain cations (b) Draw and label an electrolytic cell.

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**Question 61**
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(a) Define Young modulus of elasticity;

(b) A spiral spring extends from a length of 10.0 cm to 10.01 cm when a force of 20 N is applied on it. Calculate the force constant of the spring.

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**Question 62**
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A ball is projected specific latent heat of ice = 3.4 x 10\(^{2}\) Jg\(^{-1}\) horizontally from a height of 20m above the ground specific heat capacity of water = 4.2 Jg\(^{-1}\) K\(^{-1}\) with an initial velocity of 0.4ms\(^{-1}\). Calculate the horizontal distance moved by the ball before hitting the ground. [g = 10ms\(^{-1}\)]

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**Question 63**
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(a) Define elastic limit

(b) State Hookes laws of elasticity

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**Question 64**
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Using the kinetic theory of matter, explain the definite structure of solids.

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**Question 65**
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(a) Explain (i) refraction of a wave;

(ii) critical angle

(b) State two conditions necessary for (i) total internal reflection of a wave to occur

(ii) interference wave patterns to be formed

(c) The distance between two successive crests of a water wave travelling at 3.6ms\(^{-1}\) is 0.45m, calculate the frequency of the wave

(d) A ray of light is incident at an angle of 30° at an air-glass interface.

(i) Draw a ray diagram to show the deviation of the ray in the glass.

(ii) Determine the angle of deviation. [Refractive index of glass = 1.50]

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**Question 66**
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**TEST OF PRACTICAL KNOWLEDGE QUESTION**

You have been provided with a retort stand, clamp and boss, a set of masses, a spiral spring, stopwatch, split cork, and other necessary apparatus. Using the diagram above as a guide, carry out the following instructions;

- Suspend the spiral spring vertically as shown in the diagram.
- Suspend a mass hanger on the free end of the spiral spring and add a mass, m 50.0g to the hanger.
- Pull the hanger gently downwards and release to set it into vertical 0scillations.
- Determine the time, t, for 20 complete oscillations.
- Evaluate the period, t, of the oscillation. Also, evaluate T\(^{2}\).
- Repeat the procedure for four other values of m= 70, 90, 110, and 130g. In each case, determine t and evaluate T and T\(^{2}\). Tabulate your readings.
- Plot a graph of T\(^{2}\) on the vertical axis against m on the horizontal axis.
- Determine the slope, s, of the graph and the intercept, l, on the vertical axis.
- Evaluate k = 4\(\frac{\pi ^{2}}{s}\), Take t = \(\frac{22}{7}\)
- State two precautions taken to ensure accurate results.

(b)i. Define Young modulus and force constant.

ii. A force of magnitude 500N is applied to the free end of a spiral spring of force constant 1.0 x 10\(^{4}\) Nm\(^{-1}\). Calculate the energy stored in the stretched spring.

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**Question 67**
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**TEST OF PRACTICAL KNOWLEDGE QUESTION**

You are provided with a potentiometer **XY**, a voltmeter, **V**, a standard resistor **R**, an accumulator, **E **a plug key, **K**, a jockey, and connecting wires.

- Connect a circuit as shown in the diagram above.
- Close the key and use the jockey to make contact with the potentiometer with
**XY**at a point**N**such that=*l***XN**= 15cm. - Read and record the value of the potential difference
**V**on the voltmeter. - Evaluate
*l*\(^{-1}\) and V\(^{-1}\). - Repeat the procedure for five other values of I= 25, 35, 45, 55, and 65cm respectively. Read and record the value of
**V**and evaluate V\(^{-1}\) and*l*\(^{-1}\) in each case. Tabulate your readings. - Plot a graph V\(^{-1}\) on the vertical axis against
*l*\(^{-1}\)on the horizontal axis starting both axes from the origin (0,0). - Determine the slope, s, of the graph.
- Evaluate k = \(\frac{1}{s}\)
- State two precautions taken to ensure accurate re- results.

(b)i. State four factors on which the resistance of a wire depends.

ii. A resistance Wire of length 100cm is connected in a circuit. If the resistance per unit length of the wire is 0.02 \(\Omega\)cm\(^{-1}\), how much heat would be produced in the wire if a voltmeter connected across its ends indicates 1.5V while the current runs for 1 minute?

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**Question 68**
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Describe, with the aid of a diagram, how a wave can be plane polarized.

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