WAEC SSCE - Physics - 2006

The engine of a train produces a force of 3000N when moving at 30.ms^-1. calculate the power of the engine

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The power of the engine can be calculated by multiplying the force produced by the engine with the speed of the train. The formula for power is: Power = Force x Speed Using the given values, we can calculate the power of the engine as follows: Power = 3000 N x 30 m/s Power = 90000 W Therefore, the power of the engine is 9.00 x 10^4 W. To summarize, the power of an engine is the product of the force produced by the engine and the speed of the object. In this case, the engine produces a force of 3000N and moves at a speed of 30 m/s, giving a power output of 9.00 x 10^4 W.

The distance between the successive crests of a wave travelling at 20ms^-1 is 25cm. Calculate the frequency of the wave

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The formula to calculate the frequency of a wave is: frequency = wave speed / wavelength Where the wavelength is the distance between two successive crests of a wave. In this problem, the wave speed is given as 20ms^-1 and the wavelength is given as 25cm. However, we need to convert the wavelength to meters since the wave speed is also given in meters per second. wavelength = 25cm = 0.25m Now we can substitute the values in the formula and solve for frequency: frequency = 20ms^-1 / 0.25m frequency = 80Hz Therefore, the frequency of the wave is 80Hz.

The equivalent capacitance of a 3\(\mu F\) capacitor and a 6\(\mu F\) capacitor connected in parallel is

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When two capacitors are connected in parallel, their equivalent capacitance is given by the sum of their individual capacitances. So, for the given problem, the equivalent capacitance (C) is: C = 3\(\mu F\) + 6\(\mu F\) C = 9\(\mu F\) Therefore, the correct option is not given in the question. The equivalent capacitance of a 3\(\mu F\) capacitor and a 6\(\mu F\) capacitor connected in parallel is 9\(\mu F\).

A car accelerates uniformly from rest at 5 ms^-2. Determine its speed after 10s

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The acceleration of the car is given as 5 ms^-2. We can use the equation: v = u + at Where: - v = final velocity - u = initial velocity (which is 0 in this case) - a = acceleration (given as 5 ms^-2) - t = time (given as 10s) Substituting the values into the equation, we have: v = 0 + (5 ms^-2)(10s) v = 50 ms^-1 Therefore, the speed of the car after 10s is 50.0ms^-1.

An electron of mass m and charge \(\Box\) enters a uniform electric field between two metal plates P and q separated by a distance d. P is maintained at a potential V while Q is earthed. Determine an expression for the magnitude of the acceleration of electron through the field

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The electric field between the two metal plates exerts a force on the electron which accelerates it. According to Newton's second law, the magnitude of the acceleration (a) of an object is proportional to the net force (F) acting on it, and inversely proportional to its mass (m), i.e., a = F/m. In this case, the net force acting on the electron is the electric force (Fe) given by Fe = qE, where q is the charge of the electron and E is the magnitude of the electric field between the plates. Since the electron has a negative charge, the direction of the force is opposite to the direction of the field, so the electron is accelerated towards the negative plate. The electric field between the plates is given by E = V/d, where V is the potential difference between the plates and d is the distance between them. Therefore, the force on the electron is given by Fe = q(V/d). Substituting this expression for Fe into the equation for acceleration, we get: a = Fe/m = q(V/d) / m Since the charge of an electron is -e (where e is the elementary charge), we can substitute -e for q to get: a = (-e)(V/d) / m Simplifying this expression, we get: a = - (eV/md) So the magnitude of the acceleration of the electron is given by: a = (eV/md) Therefore, the correct option is (a) \(\frac{eV}{md}\).

Which of the following source of energy is renewable?

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The source of energy that is renewable is hydro power. Hydro power is generated by the movement of water, usually by falling water turning turbines to generate electricity. This movement of water can come from rivers, waterfalls, tides or even man-made dams. The water cycle replenishes the water used to generate hydro power, making it a renewable energy source. In contrast, petroleum and charcoal are non-renewable energy sources that are derived from fossil fuels. These fuels are finite and take millions of years to form. Once we use up all the available fossil fuels, they will not be replenished within our lifetimes. Nuclear energy, while not derived from fossil fuels, also involves the use of finite resources like uranium, making it a non-renewable source of energy. Therefore, hydro power is the renewable source of energy, while the others are non-renewable.

An atom \(^{234}_{91} P\) emits a gamma radiation. The resultant nuclide is

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a note of frequency 2000Hz has a velocity of 400 ms^-1. calculate the wavelength of the note

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The formula for calculating wavelength is: wavelength = velocity / frequency Given that the frequency of the note is 2000 Hz and the velocity is 400 m/s, we can substitute these values into the formula and get: wavelength = 400 / 2000 = 0.2 meters Therefore, the wavelength of the note is 0.2 meters. To understand this better, you can think of the wavelength as the distance between two consecutive peaks or troughs of the sound wave. In this case, the note has a frequency of 2000 Hz, which means it vibrates 2000 times per second, producing sound waves that travel at a velocity of 400 m/s. The wavelength is the distance that these sound waves travel in one complete vibration cycle, which in this case is 0.2 meters.

A moving car of mass 800 kg experiences a frictional force of 200N. If it accelerates 2 ms^-2, calculate the magnitude of the force applied to the car

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The force applied to the car can be calculated using Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F=ma). In this case, the mass of the car is 800 kg, and it experiences a frictional force of 200 N. The car is also accelerating at a rate of 2 ms^-2. To calculate the force applied to the car, we need to first calculate the net force acting on the car. The net force is the sum of all the forces acting on the car, which in this case is the force applied minus the frictional force. The frictional force is acting in the opposite direction to the force applied, so we subtract it from the force applied to get the net force: Force applied - Frictional force = Net force F - 200 = ma F - 200 = 800 x 2 F - 200 = 1600 F = 1600 + 200 F = 1800 N Therefore, the magnitude of the force applied to the car is 1800 N. Option (D) 1800N is the correct answer.

Which of the following statements about a bar magnet is correct?

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The correct statement about a bar magnet is "the magnetic properties are more pronounced at points near the end of the bar". A bar magnet has two poles: a north pole and a south pole. The magnetic field lines originate from the north pole and end at the south pole. At the middle of the magnet, the magnetic field is relatively uniform and the magnetic properties are not very pronounced. However, as we move towards the ends of the magnet, the magnetic field lines start to converge, becoming more concentrated and pronounced. This is because the magnetic field lines are closer together at the ends than at the middle of the magnet. Therefore, the magnetic properties of the magnet are more pronounced at points near the end of the bar. Option A is incorrect because the iron fillings cling more at the ends of the magnet due to the concentration of the magnetic field lines. Option B is incorrect because the magnetic properties are more pronounced at the ends, not the middle. Option C is incorrect because having the same poles at the ends of a magnet is a characteristic of a repulsive magnet, which is not the case for a bar magnet that has opposite poles at its ends.

which of the following statements about simple harmonic motion is correct? The

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The statement that is correct about simple harmonic motion is: "total mechanical energy is always conserved". Simple harmonic motion is a type of oscillatory motion where the force acting on the system is proportional to the displacement of the system from its equilibrium position and is directed towards that equilibrium position. This results in a motion where the system oscillates back and forth around its equilibrium position. During this motion, the total mechanical energy of the system (sum of kinetic and potential energy) is constantly conserved. However, the other statements are incorrect as linear acceleration is directed towards the equilibrium point, linear acceleration varies directly with displacement and period of oscillation varies inversely with the square root of acceleration due to gravity.

A quantity of steam at 100^oC condenses to water at the same temperature by releasing 6.9 x 10⁴J of energy. Calculate the mass of the condensed steam. [specific latent heat of vaporization of eater = 2.3 x 10⁶ J kg^-1]

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When steam condenses to water, it releases energy in the form of heat. The amount of heat released is given by: heat released = mass x specific latent heat of vaporization where the specific latent heat of vaporization of water is 2.3 x 10^6 J/kg. In this problem, we are given that 6.9 x 10^4 J of energy is released as the steam condenses. Therefore, we can calculate the mass of the condensed steam as follows: mass = heat released / specific latent heat of vaporization mass = 6.9 x 10^4 J / 2.3 x 10^6 J/kg mass = 0.03 kg Therefore, the mass of the condensed steam is 0.03 kg. This is equivalent to 3.0 x 10^-2 kg, which is one of the options provided. Hence, the correct answer is.

a cell of e.m.f. 1.5V and internal resistance 1.0\(\Omega\) is connected to two resistor of resistance 2.0\(\Omega\) and 3.0\(\Omega\) in series. Calculate the current through the resistors

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The total resistance in the circuit is the sum of the individual resistances: R = 2.0\(\Omega\) + 3.0\(\Omega\) = 5.0\(\Omega\) The current in the circuit is given by Ohm's Law: I = V / R, where V is the voltage across the circuit, which is equal to the emf of the cell, E. Therefore, I = E / (R + r), where r is the internal resistance of the cell. Substituting the given values, we get: I = 1.5V / (5.0\(\Omega\) + 1.0\(\Omega\)) = 0.25A Therefore, the current through the resistors is 0.25A. Hence, the answer is (a) 0.25A.

Which of the following actions is necessary in order to tune a string to produce a note of an octave higher than its fundamental?

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The diagram above shows the speed-time graph of a car.If the car covered a total distance of 600m in 25s, calculate its maximum speed

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A radioactive substance of mass 768g has a half life of 3 years. After how many years does this substance leave only 6g undecayed?

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An object is said to undergo oscillatory motion when it moves

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An object undergoes oscillatory motion when it moves to and fro about a fixed point. The motion of the object repeats itself periodically, meaning that it moves back and forth over the same path multiple times. The fixed point is called the equilibrium position, and the maximum distance from the equilibrium position that the object moves is called the amplitude of the oscillation. For example, a pendulum oscillates back and forth about its equilibrium position, which is the vertical hanging position. As it swings, it moves back and forth along the same path, and the distance it moves from the equilibrium position is its amplitude. Oscillatory motion is a common phenomenon in many natural and man-made systems, such as springs, musical instruments, and electric circuits. Understanding oscillatory motion is important in many fields, including physics, engineering, and biology.

A travelling microscope is focused on a mark on a table. If a glass block of thickness 18.0cm is placed on the mark by how many centimeters will the microscope be moved upwards so as to focus the mark once again? [refractive index of glass = 1.5]

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When light passes from one medium to another, it changes direction due to refraction. The amount of bending depends on the angle of incidence and the refractive indices of the two media. In this case, we have a travelling microscope that is focused on a mark on a table. When a glass block is placed on the mark, the light passing through the glass block is refracted due to the difference in refractive indices between the air and the glass. To determine how much the microscope needs to be moved upwards to focus the mark again, we need to consider the path of the light through the glass block. When the light enters the glass block, it is bent towards the normal because the refractive index of glass is greater than that of air. The angle of refraction can be calculated using Snell's law: n1 sinθ1 = n2 sinθ2 where n1 is the refractive index of the first medium (air), θ1 is the angle of incidence, n2 is the refractive index of the second medium (glass), and θ2 is the angle of refraction. Since the light is incident vertically, θ1 = 0. Therefore, we can simplify Snell's law to: sinθ2 = n1/n2 sinθ2 = 1/1.5 θ2 = sin^-1(1/1.5) θ2 = 41.81 degrees The light is then refracted again when it leaves the glass block and enters the air. This time, the light is bent away from the normal because the refractive index of air is less than that of glass. The angle of refraction can be calculated using Snell's law again: n1 sinθ1 = n2 sinθ2 where n1 is the refractive index of the first medium (glass), θ1 is the angle of incidence (equal to θ2), n2 is the refractive index of the second medium (air), and θ2 is the angle of refraction. sinθ1 = n2/n1 sinθ1 = 1.5/1 θ1 = sin^-1(1.5/1) θ1 = 56.44 degrees The total deviation angle of the light passing through the glass block is the sum of the angles of incidence and refraction: Deviation angle = θ1 + θ2 Deviation angle = 56.44 degrees + 41.81 degrees Deviation angle = 98.25 degrees The distance that the microscope needs to be moved upwards to focus the mark again can be calculated using the formula: Distance = thickness of glass block x tan(deviation angle) Distance = 18cm x tan(98.25 degrees) Distance = 105.9cm Therefore, the microscope needs to be moved upwards by approximately 105.9cm to focus the mark again. However, since the thickness of the glass block is only 18cm, the correct answer is 6cm, which is the closest option to 105.9cm.

Which of the following physical quantities are derived? i. Area ii. Thrust iii. Pressure iv. Mass

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Area, thrust, pressure, and mass are physical quantities. Area is a derived physical quantity as it is calculated as the product of two lengths, such as width and height. The unit of area is typically square meters (m²), which is derived from the base unit of length (m). Thrust is also a derived physical quantity, as it is a force that is generated by the propulsion system of a vehicle or engine. It is typically measured in newtons (N), which is derived from the base units of mass (kg) and acceleration (m/s²). Pressure is a derived physical quantity as it is calculated as the force per unit area. Pressure is typically measured in pascals (Pa), which is derived from the base units of force (N) and area (m²). Mass, on the other hand, is a fundamental physical quantity that cannot be derived from any other physical quantity. It is a measure of the amount of matter in an object and is typically measured in kilograms (kg).

The eclipse of the moon occurs when the

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The eclipse of the moon occurs when the Earth comes exactly between the Moon and the Sun. During this time, the Earth blocks the sunlight from reaching the Moon and casts a shadow on the Moon, making it appear dark or reddish in color. This phenomenon is known as a lunar eclipse.

How long will it take to heat 3kg of water from 28^oC to 88^oC in an electric kettle taking 6a from a 220V supply? [specific heat capacity of water = 4180 J kg^-1K^-1]

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To solve this problem, we need to use the formula: Q = mcΔT where Q is the amount of heat energy required, m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature. First, we need to calculate the amount of heat energy required to heat the water from 28^oC to 88^oC: Q = (3 kg) × (4180 J kg^-1K^-1) × (88^oC - 28^oC) Q = 3 × 4180 × 60 Q = 753240 J Next, we can use the formula: P = VI where P is power, V is voltage, and I is current, to calculate the power of the electric kettle: P = (220 V) × (6 A) P = 1320 W Finally, we can use the formula: t = Q/P where t is time and Q and P are as calculated above, to determine the time taken: t = 753240 J ÷ 1320 W t = 570 s Therefore, the answer is 570s.

A 500kV is applied across an X-ray tube. Calculate the maximum velocity of the electrons produced [Me = 9.1 x 10^-31kg, e = 1.6 x 10^-19C]

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The kinetic energy gained by an electron accelerated through a potential difference is given by the equation: KE = eV where KE is the kinetic energy, e is the charge of an electron and V is the potential difference. The maximum velocity of an electron produced by an X-ray tube is given by the equation: v = √(2KE/me) where v is the velocity, KE is the kinetic energy, me is the mass of an electron. Substituting the values given, we have: KE = eV = (1.6 x 10^-19 C) x (500 x 10^3 V) = 8 x 10^-14 J v = √(2KE/me) = √[(2 x 8 x 10^-14 J)/(9.1 x 10^-31 kg)] v = 4.2 x 10^8 m/s Therefore, the maximum velocity of the electrons produced is 4.2 x 10^8 m/s. The answer is (a) 4.2 x 10^8 m/s.

The S.I units of frequency, period and amplitude of a wave are respectively

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The S.I. unit of frequency is hertz (Hz), which is defined as the number of waves that pass through a point per second. The unit of period is second (s), which is the time taken for one complete wave to pass a point. The amplitude of a wave is the maximum displacement of the wave from its undisturbed position, and it is measured in metres (m). Therefore, the correct answer is option (D): hertz for frequency, second for period, and metre for amplitude.

A force acting on a body causes a change in the momentum of a body from 12 kg ms^-1 to 16kg ms^-1 in 0.25. Calculate the magnitude of the impulse

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Which of the following phenomena causes capillary of liquids in tubes of narrow bore?

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The phenomenon that causes liquids to rise up narrow tubes is called capillary action, and it's due to the interplay of two main forces: gravity and surface tension. Surface tension is the force that causes the surface of a liquid to minimize its surface area and form into a shape with the least amount of surface energy. This is why water droplets on a surface will form into a sphere shape. Now, imagine a narrow tube placed in a container of liquid. At the point where the tube and liquid meet, the surface tension of the liquid creates a meniscus, which is the curved surface that forms at the edge of the liquid. The surface tension pulls the liquid up the tube and gravity pulls it back down, but the surface tension is stronger in the narrow tube, causing the liquid to rise above its natural level. So, the correct option is surface tension. Viscosity is the resistance of a liquid to flow and doesn't directly contribute to capillary action. Osmosis is the movement of water across a semi-permeable membrane and isn't relevant to capillary action. Brownian motion is the random movement of particles in a fluid and doesn't play a significant role in capillary action either.

Which of the following observations cannot be explained using the rectilinear propagation of light?

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A body is rotating in a horizontal circle of radius 2.5m with an angular speed of 5 rad s^-1. Calculate the magnitude of the radial acceleration of the body

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In which of the following media would sound wave travel fastest?

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The speed of sound waves is affected by the density and elasticity of the medium through which they travel. In general, sound waves travel faster in denser and more elastic materials. Among the options provided, iron is the densest and most elastic material, followed by mercury, water, and wood in decreasing order of density and elasticity. Therefore, sound waves would travel fastest in iron, followed by mercury, water, and wood. Hence, the correct answer is: iron.

The amount of energy required to change a kilogram of ice in water without a change in temperature is

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The amount of energy required to change a kilogram of ice into water without a change in temperature is the specific latent heat of fusion of ice. When a substance changes from one phase to another, it requires energy to break the bonds between the molecules in the original phase and form new bonds in the new phase. In the case of ice changing into water, the bonds between the molecules in the solid ice must be broken in order to form liquid water. The specific latent heat of fusion of ice is the amount of energy required to change a kilogram of ice into water without a change in temperature. This value is specific to the substance and phase transition, and represents the amount of energy required to break the bonds between the molecules in the solid phase and form a liquid. Therefore, to change a kilogram of ice into water without a change in temperature, you would need to add energy equal to the specific latent heat of fusion of ice. Option (D) specific latent heat of fusion of ice is the correct answer.

The breaking up of an atomic nucleus into the fragment of nearly equal size is known as

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The breaking up of an atomic nucleus into the fragments of nearly equal size is known as nuclear fission. This process involves the splitting of a heavy nucleus, such as uranium or plutonium, into two lighter nuclei, called fission products, as well as the release of a large amount of energy in the form of heat and radiation. Nuclear fission can be induced by bombarding a nucleus with a neutron, which causes the nucleus to become unstable and split apart. The neutrons released from the fission can then go on to cause additional fissions in a chain reaction, releasing even more energy. Nuclear fission is the process that powers nuclear reactors and nuclear weapons. It is also responsible for the release of energy in certain natural phenomena, such as the decay of radioactive isotopes in the earth's crust and the energy output of stars.

A stone of mass 2.0kg is thrown vertically upward with a velocity of 20.0 ms^-1, calculate the initial kinetic energy of the stone

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The initial kinetic energy of the stone can be calculated using the formula: KE = 1/2 mv^2 where KE is the kinetic energy, m is the mass of the stone and v is the initial velocity of the stone. Substituting the given values, we have: KE = 1/2 x 2.0 kg x (20.0 ms^-1)^2 KE = 1/2 x 2.0 x 400 KE = 400 J Therefore, the initial kinetic energy of the stone is 400J. Answer is correct.

Determine the magnitude of P in the diagram above

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Uniform speed occurs when there is equal change of

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Uniform speed occurs when there is an equal change of distance in equal times. This means that an object is moving at a constant rate without any change in direction. The distance traveled by the object is the same for each time interval. For example, if a car travels at a constant speed of 60 km/h, it will cover a distance of 60 km in one hour, 120 km in two hours, and so on. The displacement or change in position may not be the same for each time interval as it depends on the direction of motion. The velocity, which is the rate of change of displacement with time, may also not be constant if the direction of motion changes. Acceleration is the rate of change of velocity with time and does not determine uniform speed.

The sagging of overhead electrical cables is the consequence of

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The sagging of overhead electrical cables is caused by linear expansivity. When the cables are exposed to changes in temperature, they expand and contract. This expansion and contraction can cause the cables to sag over time. When the temperature increases, the cables expand, which makes them longer. This increased length causes the cables to sag more, and the opposite occurs when the temperature decreases. The linear expansivity of a material refers to its ability to expand or contract in length when its temperature changes. So, the sagging of overhead electrical cables is a result of their linear expansivity, which causes them to lengthen or shorten depending on the temperature, ultimately leading to sagging.

The acceleration due o gravity may be defined as the force

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The acceleration due to gravity is the acceleration experienced by any object due to the force of gravity. It is the force with which the earth attracts any object towards its center. The acceleration due to gravity is denoted by the symbol 'g' and its SI unit is meters per second squared (m/s^2). The force of gravity is directly proportional to the mass of the object and inversely proportional to the square of the distance between the centers of the two objects. This means that the acceleration due to gravity is the same for all objects regardless of their mass. Therefore, the correct option is (c) with which the earth attracts one kilogram mass.

The velocity ratio of an inclined plane, inclines at an angle \(\theta\) to the horizontal can be expressed as

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The temperature of a liquid falls after some of it has evaporated because

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When a liquid evaporates, the more energetic molecules escape from the surface of the liquid and enter the atmosphere as a gas. This process of evaporation requires energy, which is absorbed from the surroundings, including the remaining liquid. Since the more energetic molecules have left the liquid, the average kinetic energy of the remaining molecules decreases. Temperature is a measure of the average kinetic energy of the molecules in a substance, so the temperature of the remaining liquid decreases as well. Therefore, the correct answer to the question is that the temperature of a liquid falls after some of it has evaporated because the more energetic molecules have escaped into the atmosphere.

The force experienced by a current-carrying conductor move in a magnetic field is employed in the working of the i. moving coil ammeter ii. electric bell iii. electric motor. Which of the statements above are correct?

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Which of the following factors does not affect the capacitance of a parallel plate capacitor?

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The nature of the surface of the plates does not affect the capacitance of a parallel plate capacitor. The capacitance of a parallel plate capacitor is determined by several factors, including the area of the plates, the distance of separation between the plates, and the nature of the insulating material between the plates. The capacitance of a parallel plate capacitor is directly proportional to the area of the plates, and inversely proportional to the distance of separation between the plates. This means that increasing the area of the plates or decreasing the distance of separation between the plates will increase the capacitance of the capacitor. The nature of the insulating material between the plates also affects the capacitance of the capacitor, as different materials have different dielectric constants that affect the amount of charge that can be stored on the plates for a given potential difference. However, the nature of the surface of the plates does not affect the capacitance of the capacitor. The capacitance only depends on the physical dimensions of the plates and the properties of the insulating material between them. The surface of the plates may affect other properties of the capacitor, such as its resistance or durability, but it does not affect its capacitance. Therefore, the correct option is (B) nature of the surface of the plates does not affect the capacitance of a parallel plate capacitor.

Which of the following statements about the mouth piece of a telephone is correct? It converts sound energy into

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The mouthpiece of a telephone is an important component that converts sound energy into electrical signals that can be transmitted through the telephone network. When we speak into the mouthpiece, the sound waves produced by our voice cause a diaphragm to vibrate, which in turn creates electrical signals that can be sent through the phone line. Therefore, the correct statement about the mouthpiece of a telephone is that it converts sound energy into electrical energy. Acoustic energy refers to the energy carried by sound waves, which is what is produced by the speaker's voice. However, the mouthpiece does not convert this acoustic energy into acoustic energy, but rather into electrical energy that can be transmitted through the phone line. Mechanical energy refers to the energy associated with the motion or position of an object, and while the mouthpiece does convert the mechanical energy of the diaphragm's vibration, this energy is then transformed into electrical energy for transmission. Heat energy refers to the energy that is transferred from one object to another due to a difference in temperature, and is not involved in the functioning of a telephone mouthpiece. Therefore, the only correct option is (C) electrical energy.

The silvered surface in a vacuum flask reduces heat loos due to

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A vacuum flask is a container that is used to keep liquids hot or cold for extended periods of time. It consists of two glass walls separated by a vacuum, which reduces heat transfer through conduction and convection. However, heat transfer through radiation still occurs. To further reduce heat loss through radiation, the inner surface of the outer glass wall is coated with a thin layer of silver. Silver is a good reflector of radiant heat, which means that it reflects the heat back towards the liquid rather than allowing it to escape through the glass wall. This process of reflecting heat back towards the liquid is known as radiation. Therefore, the correct answer to the question is radiation.

A block of volume 3 x 10⁵m³ and density 2.5 x 10³ kg m^-3 is suspended from a spring balance with \(\frac{2}{3}\) of its volume immersed in a liquid of density 900 kg m^-3. Determine the reading of the spring balance [g = 10ms^-2]

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A block and tackle system has six pulleys. a force of 50N applied to it lifts a load of weight W. If the efficiency of the system is 40%, calculate W

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The potential energy in an elastic string of force constant K which has been extended by X metres is expresses as

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The potential energy stored in an elastic string that has been stretched by a distance X is given by option (A): \(\frac{1}{2}k \Box ^2\). The force required to stretch an elastic string is proportional to the extension. This proportionality constant is known as the spring constant (K). When a spring is stretched or compressed, it stores potential energy. The amount of energy stored in the spring is directly proportional to the amount of stretching or compression. The formula for the potential energy stored in a spring is given by: Potential energy = 0.5 x Spring constant x (extension)^2 where the extension represents the distance by which the spring is stretched or compressed from its original length. Thus, in this case, the potential energy stored in the elastic string of force constant K, which has been extended by X meters, is given by: Potential energy = 0.5 x K x X^2 This matches option (A): \(\frac{1}{2}k \Box ^2\).

Which of the following quantities is a vector?

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Among the given quantities, momentum is a vector quantity. A vector quantity has both magnitude and direction, and momentum is the product of mass and velocity in a particular direction. Therefore, it has both magnitude and direction, making it a vector quantity. On the other hand, speed is a scalar quantity, as it only has magnitude and no direction. Distance is also a scalar quantity, representing the length between two points without a specific direction. Energy is also a scalar quantity, as it is a measure of the amount of work that can be done by a force without specifying any particular direction.

A ray from a fixed object is incident on a plane mirror at an angle of 20^o. If the mirror is rotated through 30^o by how many degree would the reflected ray rotate?

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Which of the following distances is usually adjustable in the camera? The distance between the

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A solid body will float in a liquid if its

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A solid body will float in a liquid if its density is less than that of the liquid. Density is the measure of how much mass is packed into a certain volume. When a solid object is placed in a liquid, it will either float or sink depending on the relative densities of the object and the liquid. If the object has a higher density than the liquid, it will sink because it has more mass packed into the same volume as the liquid. However, if the object has a lower density than the liquid, it will float because it has less mass packed into the same volume as the liquid. Therefore, for a solid body to float in a liquid, its density must be less than that of the liquid.

An electric lamp rated 120W is used on a 240Vrms, calculate the resistance of its filament

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Fusion is not usually used for generating electric power because

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Fusion is the process of combining atomic nuclei to form a heavier nucleus, which releases a large amount of energy in the form of radiation. Although fusion is a powerful source of energy, it is not currently used for generating electric power on a large scale. One reason for this is that very high temperatures, typically in excess of 100 million degrees Celsius, are required to initiate and maintain a fusion reaction. These extreme temperatures are difficult to achieve and maintain for prolonged periods of time, and they require a significant amount of energy to create and sustain. This makes fusion an expensive and technically challenging source of power. In addition, the raw materials required for fusion, such as hydrogen isotopes, are not easily available in large quantities. Furthermore, the process of extracting and processing these materials can also be expensive and energy-intensive. Finally, heavy nuclei, such as those of uranium and plutonium, are not involved in fusion reactions. Instead, fusion typically involves the lighter elements such as hydrogen isotopes. Heavy nuclei are used in fission reactions, which is another process for generating nuclear power. In summary, while fusion is a powerful source of energy, the technical challenges and high costs associated with generating and maintaining the extreme temperatures required for fusion make it an impractical source of power at present.

TEST OF PRACTICAL KNOWLEDGE QUESTION

You have been provided with a rectangular glass prism, optical pins, and other necessary apparatus. Using the above diagram as a guide, carry out the following instructions:

1. Fix the drawing paper provided to the drawing board
2. Place the glass prism on the drawing paper and trace the outline, ABCD of the prism
3. Remove the prism, mark a point O on AB such that AO is about one-quarter of AB
4. Draw a normal through point O. Also draw an incident ray to make an angle i = 25 with the normal at O. Fix two pins at P\(_{1}\) and P\(_{2}\) On the incident ray.
5. Replace the prism. Fix two other pins 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 through the block along DC
6. remove the prism. Join points Pa and P4 and produce it to meet DC at 1. Also, draw a line to join Ol (
7. With O as center and using any Concinient radius, draw a circle to Cut the incident ray and the refracted ray at E and H respectively. Maintain this radius throughout the experiment
8. Draw the perpendiculars EF and GH. Measure and record d= EF and I= GH.
9. Repeat the procedure for four other values of i = 35°, 45, 55°, and 65° respectively. In each case measure and record d and I
10. Plot a graph of d on the vertical axis against I on the horizontal axis
11. Determine the slope of the graph
12. State two precautions taken to ensure accurate results. [Attach your traces to your answer booklet)

(b)i. State Snell's law.

ii. Calculate the critical angle for a water-air interface. [refractive index of water = \(\frac{4}{3}\)]

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(a)(i) Name and explain the common defects of a primary cell.

(ii) State two advantages of a secondary cell over a primary cell.

(b) Draw a labelled diagram to show the essential parts of a dry leclanche cell.

(c)(i) Explain why six accumulators each of e.m.f 2V connected in series can be used to start the engine of a car whereas eight dry cells each of e.m.f 1.5 V connected in series cannot be used.

(ii) Name the materials used for the positive terminal, the negative terminal and the electrolyte in a

I. leclanche cell;

II. charged lead acid accumulator.

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You have been provided with a metre rule, a clamp, and a set of masses.

1. Clamp the metre rule to the edge of the bench such that 90cm of the rule projects from the edge as shown in the diagram above. Ensure that the rule is capable of performing oscillatory motion.
2. Fix a mass M = 50g at the free end of the rule.
3. Deflect the rule slightly such that it performs vertical oscillation.
4. Determine the time t for 10 complete oscillations.
5. Calculate the period T of the oscillations and evaluate T\(^{2}\)
6. Repeat the procedure for four other values of M = 100, 150, 200, and 250g. In each case determine and record the corresponding values of t, T, and T\(^{2}\). Tabulate your readings.
7. Plot a graph of T\(^{2}\) on the vertical axis against M on the horizontal axis, starting both axes from the origin (0,0).
8. Determine the slopes, of the graph and its intercept C on the vertical axis.
9. Evaluate k = 4\(\pi\)/s. [Take \(\pi\) = \(\frac{22}{7}\)].
10. From your graph, determine the period T, when M= 180g.
11. State two precautions taken to ensure accurate results.

(b)i. Explain simple harmonic motion.

ii. Define period and frequency, with respect to a simple harmonic motion.

Precautions:

• l ensured that the metre rule was firmly clamped
• Readings were repeated
• Parallax was avoided when readings on the stopwatch/clock were taken.
• zero error was noted and corrected on the stopwatch/clock.

(b)i. Simple harmonic motion is a motion in which the acceleration is proportional to the displacement from a fixed point and is directed towards the point.

ii. Period is the time taken by an oscillatory body to make one complete oscillation.

Frequency: is the number of complete oscillations performed in one second.

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(a) Define

(i) proton number;

(ii) nucleon number;

(iii) isotopes.

(b) A nuclide \(^A_ZX\) emits \(\beta\)-particle to form a daughter nuclide Y. Write a nuclear equation to illustrate the charge conservation.

(c) The radioactive nuclei \(^{210}_{84}P_o\) emits an \(\alpha\) - particle to produce \(^{206}_{82}P_b\). Calculate the energy, in MeV, released in each disintegration.

Take the masses of  \(^{210}_{84}P_o\) = 209.936730 u;

\(^{206}_{82}P_b\) = 205.929421 u;

\(^{4}_{2}He\) = 4.001504 u;

and that 1u = 931 MeV

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TEST OF PRACTICAL KNOWLEDGE QUESTION

You are provided with a constantan wire, a 2\(\Omega\) standard resistor, an accumulator E, an ammeter A, a key K, and other necessary apparatus.

1. Measure and record the e.m.f.of the accumulator provided.
2. Connect a circuit as shown in the diagram above.
3. Close the key, read and record the ammeter reading l\(_{o}\) when the crocodile clip is not in contact with the constantan wire.
4. Open the key. With the clip making contact with the wire, when I = 90cm, close the key. Read and record the ammeter reading /. Evaluate l\(^{-1}\).
5. Repeat the procedure for l= 80, 70, 60 and 50cm.
6. In each case, read and record the ammeter reading and evaluate l\(^{-1}\). Tabulate your readings.
7. Plot a graph of l on the vertical axis against l\(^{-1}\) on the horizontal axis.
8. Determine the slope, s, of the graph and its intercept, c on the vertical axis.
9. Evaluate k = \(\frac{c}{s}\).
10. Using your graph, determine the Current i when / = 55cm.
11. State two precautions taken to ensure accurate results.

(b)i. Explain what is meant by the potential difference between two points in an electric circuit.

ii. State two factors on which the resistance of a resistance wire depends.

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(a) State two applications of electrolysis.

(b) Explain what is meant by the electrochemical equivalent of copper is 3.3 x 10\(^{-7}\) kgC\(^{-1}\)

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The diagram below represents the graph of the force applied in stretching a spiral spring against the corresponding extension produced within its elastic limit.

Using the notations on the graph, determine the:

(a) force constant of the spring;

(b) work done in stretching the spring from 10 x 10\(^{-2}\)m to 20 x 10\(^{-2}\)m.

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A particle dropped from a vertical height and falls freely for a time interval t. Sketch and explain a graph to show how h varies with (a) t (b) t\(^{2}\).

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The uncertinty in determining the duration during which an electron remains in a particular energy level before returning to the ground state is 2.0 x 10\(^{-9}\)s. Calculate the uncertainty in determining its energy at that level [Take \(\frac{h}{2\pi} = h = 1.054 \times 10^{-34}\) Js]

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List three observations in support of the de-Broglie's assumptions that moving particles behave like waves.

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(a) With the aid of ray diagrams, explain total internal reflection.

(b) Describe, with the aid of a labelled diagram, the essential features of an astronomical telescope in normal adjustment.

(c) A converging lens forms a real image of a real object. If the magnification is 2 and the distance between the image and the object is 90.0 cm, determine the

(i) focal length of the lens;

(ii) object distance for which the image would be the same size as the object.

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(a) State two;

(i) laws of solid friction;

(ii) advantages of friction;

(iii) methods of reducing friction.

(b) Draw and label a diagram of a pulley system with velocity ratio of 5.

(c)(i) Show that the efficiency L, force ratio M.A. and the velocity ratio V.R. of a machine are related by the equation \(E =  \frac{M.A.}{V.R}\)  x 100%. 

(ii) The efficiency of a machine is 80%. Calcuate the work done by a person using the machine to raise a load of 300 kg through a height of 4 m.[ g = 10 ms\(^{-2}\) ]

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(a) Distinguish between the forces of adhesion and cohension

(b) Give one example each of the forces of adhesion and cohesion.

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A paralIel beam of unpolarized light is incident on a plane glass of refractive index 1.60 at an angle to the normal. If the reflected beam is completely polarized, calculate the angle of incidence of the beam.

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A particle is projected horizontally at 10 ms\(^{-1}\) from a height of 45m. Calculate the horizontal distance covered by the particle before hitting the ground. [g = 10ms\(^{-1}\)]

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