WAEC SSCE - Physics - 2001

The amplitude of a particle executing simple harmonic motion in 5cm while its angular frequency is 10 rad s^-1. calculate the magnitude of the maximum acceleration of the particle

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The maximum acceleration of a particle in simple harmonic motion is given by the product of the square of the angular frequency and the displacement of the particle from the equilibrium position. That is, a_max = -ω²A Where, A is the amplitude of the particle, and ω is the angular frequency. Substituting the given values, we get: a_max = - (10 rad/s)² x 0.05 m a_max = - 5 m/s² or 5 ms^-2 Since the maximum acceleration is a scalar quantity, we take its magnitude, which is simply 5 ms^-2. Therefore, the correct option is 5.00ms^-2.

The time rate of change of momentum is

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The time rate of change of momentum is called "force". Force is a vector quantity that causes an object to accelerate or change its velocity. When a force acts on an object for a certain amount of time, it produces a change in the object's momentum, which is called impulse. Therefore, force can also be defined as the rate of change of momentum, that is, the amount of impulse produced per unit of time.

Which of the following physical qualities affects the saturated vapour pressure of a liquid ?

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The physical quality that affects the saturated vapour pressure of a liquid is temperature. Saturated vapour pressure is the pressure exerted by the vapour present in a system at equilibrium with its condensed phase, usually a liquid. As temperature increases, the average kinetic energy of the liquid molecules increases, causing more molecules to escape from the liquid phase and enter the gas phase. This leads to an increase in the number of gas molecules, which in turn results in an increase in pressure. As a result, the saturated vapour pressure of a liquid increases with increasing temperature, and decreases with decreasing temperature. Therefore, temperature is the correct answer. The other options - volume, mass, and density - do not directly affect the saturated vapour pressure of a liquid.

What is the total energy stored by the capacitors?

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An electric bulb is rated 60W, 220V. Calculate the resistance of its filament when it is operating normally

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The power of an electrical appliance can be calculated by the formula P = V\(^2\)/R, where P is the power in watts, V is the voltage in volts, and R is the resistance in ohms. In this case, the bulb is rated 60W and 220V. So, we can rearrange the formula to find the resistance: R = V\(^2\)/P. Substituting the values gives us: R = 220\(^2\)/60. Evaluating this expression gives us: R = 806.7\(\Omega\). Therefore, the resistance of the filament when the bulb is operating normally is 806.7\(\Omega\). Note: It is important to remember that the actual resistance of the filament may vary due to factors such as temperature, age, and manufacturing tolerances.

In the circuit diagram above. Calculate the energy stored in the inductor at resonance

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Electrical resistance is a property of an electrical energy to be converted into

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Electrical resistance is a property of a material to oppose the flow of electrical current through it. When electrical current flows through a conductor, some of the electrical energy is converted into other forms of energy. One of the forms of energy that can be generated is heat energy, which is the result of collisions between the electrons and the atoms in the material. This is known as Joule heating, and the amount of heat generated is proportional to the resistance of the material and the square of the current flowing through it. Therefore, when electrical energy flows through a material with resistance, some of the energy is converted into heat energy due to the resistance of the material.

The apparent weight of a body fully immersed in water is 32N and its weight in air is 96N. Calculate the volume of the body. [Density of water = 1000kgm^-3, g = 10ms^-2]

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The apparent weight of a body in a fluid is equal to the weight of the fluid displaced by the body. Using this principle, we can calculate the volume of the body as follows: Let V be the volume of the body Density of water = 1000kgm^-3 Weight of the body in air = 96N Weight of the body in water = 32N We know that: Weight of the body in air - Weight of the body in water = Upthrust = Weight of the water displaced Therefore, 96N - 32N = Weight of the water displaced 64N = Weight of the water displaced Weight of water displaced = Volume of body x Density of water x g 64N = V x 1000kgm^-3 x 10ms^-2 V = 64N / (1000kgm^-3 x 10ms^-2) V = 6.4 x 10^-3m³ Therefore, the volume of the body is 6.4 x 10^-3m³. Answer is correct.

Three identical lamps each power 100W are connected in parallel across a potential difference of 250V. Calculate the current in the circuit

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When lamps are connected in parallel, each lamp has the same voltage across it. Therefore, the potential difference across each of the three lamps is 250V. The power of each lamp is given as 100W. We know that power (P) is equal to voltage (V) multiplied by current (I), i.e., P = VI. Therefore, the current through each lamp can be calculated as I = P/V = 100/250 = 0.4 A. Since the lamps are connected in parallel, the total current in the circuit is the sum of the currents through each lamp. Hence, the total current in the circuit is 3 times the current through one lamp, which is 3 x 0.4 A = 1.2 A. Therefore, the correct option is 1.2A.

Which of the following physical processes cannot be explained by the molecular theory of matter?

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The physical processes of evaporation, thermal conduction, radiation of heat, and convectional current of fluids can all be explained by the molecular theory of matter. The theory explains that all matter is made up of tiny particles (atoms or molecules) which are constantly in motion. The motion of these particles can cause heat transfer through conduction, convection, and radiation. Evaporation is a process where some of the particles at the surface of a liquid have enough energy to escape and become a gas. Therefore, all the options listed can be explained by the molecular theory of matter.

The diagram above shows the wire of a sonometer box set into resonance by a vibrating tuning fork of frequency f, when the wire is stretched by a tension T, the resonating length of the wire is I while the wavelength of the sound produced is \(\lambda\). Which of the following statements is not correct? The wave produced on the wire is

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A block weighing 15N rests on a flat surface and a horizontal force of 3N is exerted on it. Determine the friction force on the block

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The force exerted on the block is 3N, and the block is at rest, meaning that the force of friction is equal in magnitude and opposite in direction to the applied force. Therefore, the friction force on the block is 3N. Answer: 3.0N

An object weight 10N immersed in a liquid displaces a quantity of the liquid. If the liquid displaced weighs 6N, determine the upthrust of the object

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Production of x-ray tube begins with

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An object is placed 20cm from a lens. If an image is formed on a screen 260cm away from the lens, calculate the magnification of the image

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Electrons passing through crystals are diffracted because they

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Electrons, which are usually considered as particles, can also exhibit wave-like properties, a concept known as wave-particle duality. When electrons are passed through crystals, their wave-like nature allows them to diffract, meaning they bend and scatter as they encounter the atoms in the crystal. This is similar to the way light diffracts when it passes through a narrow opening or encounters an obstacle. Therefore, the correct answer is that electrons passing through crystals are diffracted because they possess wave properties.

Dispersion of white light by a glass prism occurs because

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The volume of an ideal gas at a pressure of 77cmHg and temperature 60^oC is 24cm³. If the temperature and pressure are increased to 98^oC
and 81cmhg respectively, calculate the new volume of the gas

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Humidity is used to describe the amount of

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Humidity is used to describe the amount of water vapour present in the atmosphere. It is the measure of the water vapour content in the air, which can affect how comfortable we feel in a particular environment. Humidity can be measured in various ways, including absolute humidity, relative humidity, and specific humidity. Knowing the humidity level is important for a range of applications, from weather forecasting to indoor comfort control.

The amplitude of the motion of a body performing simple harmonic motion decreases with time because

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The magnitude of the gravitational force between two particles 0.10m apart is 10N. If the distance between them is increased to 0.20m, calculate the magnitude of the new force

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The gravitational force between two particles is given by the formula F = Gm₁m₂/r², where G is the gravitational constant, m₁ and m₂ are the masses of the particles, and r is the distance between them. In this case, the distance between the particles is initially 0.10m and the force is 10N. If the distance is increased to 0.20m, we can use the formula to calculate the new force. Let's assume that the masses of the particles remain constant. The distance between them is doubled, so the new distance is 2r = 0.20m. Plugging this into the formula and solving for the new force, we get: F' = Gm₁m₂/(2r)² = Gm₁m₂/4r² Since the masses of the particles and the gravitational constant are constants, the only thing that has changed is the distance between the particles. Therefore, the new force is proportional to 1/r². Since r has doubled, the new force will be (1/2)² = 1/4 of the original force. So, the new force is: F' = (1/4)F = (1/4)10N = 2.5N Therefore, the magnitude of the new force is 2.5N. Option (C) is the correct answer.

What is the effective capacitance in the circuit?

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Surface waves travelling in deep water at 15ms^-1 are incident at a shallow water boundary. If the angles of incidence and refraction are 45^o and 30^o respectively. Calculate the speed of the waves in shallow water

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When surface waves travelling in deep water meet a shallow water boundary, they experience a change in speed and direction. This is known as refraction. The speed of the waves is dependent on the medium they are travelling through, so when they enter shallow water, their speed will change. We can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the velocities in the two media. In this case, we have: \begin{align*} \frac{\sin i}{\sin r} &= \frac{v_i}{v_r} \\ \frac{\sin 45}{\sin 30} &= \frac{15}{v_r} \\ \frac{\sqrt{2}}{0.5} &= \frac{15}{v_r} \\ v_r &= \frac{15}{\frac{\sqrt{2}}{0.5}} \\ v_r &= 10.6\text{ms}^{-1} \end{align*} Therefore, the speed of the waves in shallow water is approximately 10.6ms^-1. The correct option is (c) 10.6ms^-1.

A simple machine with an efficiency of 75% lifts a load of 5000N when a force of 500N is applied to it. Calculate the velocity ratio of the machine

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A screw jack with a Tommy bar of length 12cm is used to raise a car through a vertical height of 25cm by turning the Tommy bar through 50 revolutions. Calculate the approximate velocity ratio of the jack [\(\pi = 3.142\)]

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A screw jack is a simple machine used to lift heavy loads with little effort. The velocity ratio of a screw jack is defined as the ratio of the distance moved by the effort (Tommy bar) to the distance moved by the load (car). In this case, the car is raised through a vertical height of 25cm by turning the Tommy bar through 50 revolutions. The distance moved by the effort is the circumference of the circle traced out by the end of the Tommy bar, which is given by: circumference = 2πr = 2 x 3.142 x 0.12m = 0.754m (approx.) Since the Tommy bar is turned through 50 revolutions, the total distance moved by the effort is: distance moved by effort = 0.754m x 50 = 37.7m (approx.) Therefore, the velocity ratio is: velocity ratio = distance moved by effort / distance moved by load = 37.7m / 0.25m = 150.8 (approx.) So the approximate velocity ratio of the jack is 151, which is closest to.

The amount of heat given out or absorbed when a substance changes its state at a constant temperature is known as

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The amount of heat given out or absorbed when a substance changes its state at a constant temperature is known as latent heat. This means that even though the temperature remains constant during the change of state, heat is still being absorbed or released. For example, when ice is melted into water or water is evaporated into steam, there is no change in temperature, but heat is still absorbed by the substance during the change of state. The latent heat is specific to the substance and the change of state, and can be calculated by multiplying the mass of the substance by the specific latent heat of the substance for the particular change of state.

The diagram above shows the wire of a sonometer box set into resonance by a vibrating tuning fork of frequency f, when the wire is stretched by a tension T, the resonating length of the wire is I while the wavelength of the sound produced is \(\lambda\). Which of the following statements about the frequency of vibration of the wire is not correct?

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Which of the following statements about sound is correct?

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Which of the following equations represents the distance x, travelled by a body moving on a straight road with a constant speed? [The other symbol have their usual meanings]

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The equation that represents the distance x, travelled by a body moving on a straight road with a constant speed is "x = Ut". In this equation, "U" represents the initial velocity of the body and "t" represents the time taken to cover the distance "x". Since the body is moving with a constant speed, its velocity remains the same throughout the journey and can be represented by "U". Therefore, the distance covered by the body can be calculated by multiplying the velocity "U" with the time taken "t", which is given by the equation "x = Ut". The other given equations represent the distance covered by a body in different scenarios like constant acceleration, initial velocity with constant acceleration, etc.

A spring balance,which is suspended from the roof of a lift, carries a mass of 1kg at its free end. If the lift accelerates upwards at 2.5ms^-2, determine the reading on the spring balance. [g = 10ms^-2]

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Which of the following statements about elastic collision is correct?

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In an elastic collision, both kinetic energy and momentum are conserved. This means that the total kinetic energy before the collision is equal to the total kinetic energy after the collision, and the total momentum before the collision is equal to the total momentum after the collision. There is no loss of kinetic energy or momentum in an elastic collision. Therefore, the statement "both kinetic energy and momentum are conserved" is correct. The other statements are incorrect as they imply a loss of either kinetic energy or momentum in an elastic collision, which is not the case.

Which of the following statements about magnetic lines of force is not correct?

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The correct option is "magnetic lines of force are closely packed together at neutral point". This statement is incorrect because neutral points are regions where the magnetic field is zero, and hence, there are no magnetic lines of force in these regions. Magnetic lines of force are an imaginary concept used to represent the direction and intensity of magnetic fields. They are assumed to be continuous and form closed loops, and are said to originate from the north pole and terminate at the south pole of a magnet. They also represent the path along which a free north pole would move in the presence of a magnetic field. Magnetic lines of force do not cross one another, and the presence of magnetic lines of force in a region indicates the presence of a magnetic field.

Which of the following statements about pressure is not correct? pressure

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Convex spherical mirrors are preferred to plane mirrors as driving mirrors because

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Convex spherical mirrors are preferred to plane mirrors as driving mirrors because they provide a wider field of view. Convex mirrors are curved outward and the reflected light rays diverge, resulting in a smaller image that appears farther away. This makes it easier for drivers to see objects behind them and in their blind spots. The wider field of view provided by convex mirrors is particularly useful for large vehicles such as buses and trucks, which have larger blind spots than smaller cars.

A nitrogen nucleus bombarded with an alpha particle produces an oxygen nucleus and a proton. The nuclear reaction for this process is \(^4_2H + ^{14}_2N \to ^{17}_{8}O + ^1_1H + Q\). Which of the following statements about the reaction is not correct?

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As the plates of a charged variable capacitor are moved closer together, the potential difference between them

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The material used for constructing the core of an electromagnet is

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The material used for constructing the core of an electromagnet is iron. An electromagnet is made by wrapping a coil of wire around a ferromagnetic core. When electric current flows through the wire, it creates a magnetic field around the wire. The ferromagnetic core helps to increase the strength of the magnetic field created by the current flowing through the wire. Iron is a good material for the core of an electromagnet because it is a ferromagnetic material that is easily magnetized and demagnetized. It also has a high magnetic permeability, which means it can conduct magnetic flux effectively.

a beam PQ pivoted at P carries a load of 80N as shown above. Calculate the effort E, required to keep it horizontal. [neglect the weight of the beam]

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A piece of cloth appears green in sunlight. When held in red light, it will appear

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When an object appears a certain color, it is because it reflects that particular color of light and absorbs all other colors. Therefore, if a piece of cloth appears green in sunlight, it means that it reflects green light and absorbs all other colors. When the same piece of cloth is held in red light, it will appear black. This is because the red light being shone on the cloth contains only red light waves, and the cloth will absorb all the red light, as it does not reflect red light. Therefore, it appears black, as there is no reflected color for our eyes to see.

An incident ray is reflected normally by a plane mirror onto a screen where it forms a bright spot. The mirror and screen are parallel and 1m apart. If the mirror is rotated through 5^o, calculate the displacement of the spot

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Calculate the reactance of the inductor in the circuit diagram shown above [\(\pi = \frac{22}{7}\)]

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The Earth's magnetic equator passes through Jos in Nigeria. At Jos. the

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The Earth's magnetic field has a north and south pole, and it is tilted with respect to the Earth's rotational axis. This means that at different points on the Earth's surface, the magnetic field has different characteristics. The magnetic equator is an imaginary line that circles the Earth, and it is the point where the magnetic field is horizontal. At Jos in Nigeria, the magnetic equator passes through, and this means that the magnetic field is horizontal at this point. Therefore, the angle of dip (the angle between the magnetic field lines and the Earth's surface) is zero.

A given mass of an ideal gas has a pressure of 500Nm^-2 at -13^oC. If its volume remains constant. Calculate its pressure at 247^oC.

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The pressure, volume, and temperature of an ideal gas are related by the ideal gas law, which is given by: P V = n R T where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the absolute temperature. If the volume of the gas remains constant, then the ideal gas law becomes: P = n R T / V Since the mass of the gas is constant, the number of moles n is also constant. Therefore, we can write: P/T = constant This means that the pressure of the gas is directly proportional to its temperature, when the volume is constant. To solve the problem, we can use the above formula to find the constant, and then use it to find the pressure at the new temperature: P1 / T1 = P2 / T2 where P1 is the initial pressure, T1 is the initial temperature, P2 is the final pressure, and T2 is the final temperature. Converting the temperatures to kelvin scale: T1 = 273 - 13 = 260 K T2 = 273 + 247 = 520 K Substituting the values: 500 / 260 = P2 / 520 Solving for P2: P2 = (500 / 260) x 520 = 1000 Nm^-2 Therefore, the pressure of the gas at the new temperature is 1000 Nm^-2. The correct option is: 1000Nm^-2.

A resistance thermometer has a resistance of 20\(\Omega\) at 0^oC and 85\(\Omega\) at 100^oC. If its resistance is 52\(\Omega\)in a medium, calculate the corresponding temperature

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If the frequency of the tuning fork at resonance is 256Hz, calculate the frequency of vibration of the wire when the tension in he wire is increased to 196N

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(a) What is electrolysis?

(b) A current of 2A is passed through a copper voltameter for 5 minutes. If the electrochemical equivalent of copper is 3.27 x 10\(^{-7}\) kg. Determine the mass of the corper deposited.

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with two wires marked P and C. a resistor R\(_{s}\) = 1\(\Omega\) and other necessary apparatus.

1. Connect R\(_{s}\) in the left-hand gap of the metre bridge, a length L= 100cm of wire P in the right-hand gap and the other apparatus as shown in the diagram: above
2. Determine the balance point B on the bridge wire AC
3. Measure and record AB =/s, and BC = /
4. Evaluate R\(_{1}\) = (\(\frac{|_{p}}{|_{s}}\))Rs
5. Repeat the procedure for four other values of L = 90, 80, 70 and 60cm. In each case obtain and record the value of |\(_{s}\) and |\(_{p}\) and evaluate R\(_{1}\) = (\(\frac{|_{p}}{|_{s}}\))Rs
6. Repeat the experiment with the second wire, Q. Obtain the value of |\(_{s}\) and |\(_{Q}\) for equal lengths of wire as used in wire P.
7. Evaluate R\(_{1}\) = (\(\frac{|_{p}}{|_{s}}\))Rs. In each case, tabulate your readings.
8. Plot a graph of R\(_{2}\) on the Vertical axis against R\(_{1}\) on the horizontal axis.
9. Determine the slope S, of the graph.
10. Evaluate the k = \(\sqrt s\).
11. State two precautions taken to ensure accurate results.

(b)i. Define the resistivity of the material of a wire.

ii. A galvanometer with a full-scale-deflection of 1.5 x10\(^{3}\). A has a resistance of 50\(\Omega\). Determine the resistance required to convert it into a voltmeter reading up to 1.5V.

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A lead shot is projected from tha ground level with a velocity u at an angle \(\theta\) to the horizontal. Given the time, t for the lead shot to reach its maximum height as; t = \(\frac{u \sin \theta}{g}\) where "g" is the acceleration of free fall due to gravity, show that the greatest height reached by the body is h\(_{\text{max}} = \frac{u^2 \sin^2 \theta}{2g}\)

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(a) What is meant by 'a beam of polarised light?

(b) With the aid of well labelled diagrams, illustrate the action in of a polaroid spectacle on a beam of sunlight.

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The above reprt the graph electron energy against the frequency of the radiation incident on a metal surface. lnterprete the;

(i) slope of the graph;

(ii) intercept, OC;

(iii) intercept, OK.

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(a) Explain how a gas can be made to conduct electricity.

(b) Name the electric charge carriers in gases.

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(a)(i) What is an echo? (ii) State two useful applications of echoes.

(iii) Why are the walls, floors and ceilings of a recording studio heavily padded?

(b)(i) Explain timbre and overtones.

(ii) What is resonance?

(c) As a ship approaches a cliff, its siren is sounded and the echo is heard in the ship after 12 seconds. 2.1 minutes later the siren was sounded again and the echo was heard 8 seconds later. If the speed of sound in air is 340 ms\(^{-1}\), calculate the velocity at which the ship was approaching the cliff.

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TEST OF PRACTICAL KNOWLEDGE QUESTION

Using the diagram as a out the guide carry out the following instructions:

1. Place the pin O horizontally inside the cylinder provided. Pour some water on the pin in the cylinder such that the length of the water column / = SO = 10.0cm, where S place the represents the water meniscus.
2. lnsert another pin, P in the cork held by the boss of the retort stand.
3. Adjust the position of P vertically upward or 0 formed by refraction at S.
4. Read and record the distance h = PO.
5. Repeat the procedure for four other values of 1= 15, 20, 25, and 30cm.
6. In each case measure and record the corresponding value of h. Tabulate your readings.
7. Plot a graph of h on the vertical axis against l on the horizontal axis.
8. Determine the slope, s, of the graph
9. Evaluate (i) K\(_{1}\) = 1 - S
                 (ii) K\(_{2}\) = \(\frac{1}{k}\)
10. State two precautions taken to ensure accurate results.

(b)i. Explain the total internal reflection of light.

ii. A rectangular glass prism of thickness 6 cm and refractive index 1.5 is placed on the page of a book. The prints on the book are viewed vertically down Determine the apparent upward displacement of the print.

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(a) The mass and wavelength of a moving electron are 9.0 x 10\(^{-31}\) kg and 1.0 x 10\(^{-10}\)m respectively. Calculate the kinetic energy of the electron. [ h = 6.6 x 10\(^{-34}\) Js]

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(a) Distinguish between stress and strain as used in elasticity.

(b) When a force of 40 N is applied to the free end of an elastic cord, an extension of 5cm is produced in the cord. Calculate the work done on the cord.

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 A ball thrown vertically upward reaches a maximum height of 50 m above the level of projection. Calculate the;

(i) time taken to reach the maximum height,

(ii) speed of the throw. [g = 10 ms\(^{-2}\)]

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(a) Explain the statement the capacitance of a capacitor is 5\(\mu\)F.

(b)(i) State the factors upon which the capacitance of a parallel plate capacitor depend.

(ii) State how the capacitance depends on each of these factors stated in (b)(i).

(c) A series arrangement of three capacitors of values 8uF, 12\(\mu\)F, and 24\(\mu\)F is connected in series with 90-V battery.

(i) Draw an open-circuit diagram for this arrangement.

(ii) Calculate the effective capacitance in the circuit.

(iii) On closed circuit, calculate the charge on each capacitor when fully charged.

(iv) Determine the p.d across the 8\(\mu\)F capacitor.

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The value of the e.m.f of a voltaic cell, which has dilute tetraoxosulphate (VI) acid as its electrolyte and copper and zinc as its electrodes becomes less with use. Explain this observation and state how it can be corrected.

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(a) In his first attempt, a long jumper took off from the springboard with a speed of 8 ms\(^{-1}\) at 30° to the horizontal. He makes a second attempt with the same speed at 45° to the horizontal. Given that the expression for the horizontal range of a projectile is \(\frac{v^2 sin \theta}{g}\) where all the symbols have their usual meanings, show that he gains a distance of 0.8576 m in his second attempt.

(b)(i) State Hooke's law of elasticity.

(ii) Describe an experiment to verify Hooke's law.

(iii) State two precautions you would take if you were to perform this experiment in the laboratory.

(c) A spiral spring of natural length 20.00 cm has a scale pan hanging freely in its lower end. When an object of mass 40 g is placed in the pan, its length becomes 21.80 cm. When another object of mass 60g Is placed in the pan, the length becomes 22.05cm. Calculate the mass of the scale pan. [g = 10 ms\(^{-2}\)]

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(a) When nitrogen (atomic mass = 14, atomic number = 7) is bombarded with neutrons, the collisions result in disintegrations in which alpha particles are produced. Represent this transmutation in a symbolic equation.

(b)(i) How does a radioactive atom differ from a stable one?

(ii) Explain 'half life'.

(iii) A sample of radioactive material has a haft life of 35 days. Calculate the fraction of the original quantity that will remain after 105 days.

(c) Light of wavelength 5.00 x 10\(^{-7}\)m is incident on a material of work function 1.90 eV. Calculate

(i) photon energy.

(ii) kinetic energy of the most energetic photo electron.

(iii) stopping potential [Plancks constant h =6.6 x 10\(^{-34}\)Js] [c= 3.0 x10\(^8\)ms\(^{-2}\), leV= 1.6 x 10\(^{19}\)J]

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