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**Question 1**
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A stationary object of mass 4kg is set in motion by a net force of 5ON. If the object attains is speed of 5ms^{-1} in time. Calculate the value of t.

**Question 2**
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The speed of sound in air is 330ms^{-1}. How far from the centre of a storm is an observer who hears a thunder clap 2s after the lightning flash? (Neglect the time taken by light to travel to the observer)

**Question 3**
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The pressure of a fixed mass of gas is 2.0 x 10^{5}Nm^{-2} at a known temperature. Assuming that the temperature remains constant, what will be the pressure of the gas if its volume is halved?

**Answer Details**

According to Boyle's law, at a constant temperature, the pressure and volume of a fixed mass of gas are inversely proportional. This means that as the volume of the gas is halved, its pressure will double. In this case, the initial pressure of the gas is 2.0 x 10^{5}Nm^{-2}. When the volume is halved, the pressure will double to 4.0 x 10^{5}Nm^{-2}. Therefore, the answer is 4.0 x 10^{5}Nm^{-2}.

**Question 4**
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Which of the following instruments produces sound by the vibration of air column?

**Answer Details**

The instrument that produces sound by the vibration of an air column is a flute. The flute is a wind instrument that produces sound by blowing air across the mouthpiece. The air column inside the flute vibrates and produces sound waves, which then travel through the instrument and out of the end, producing the sound that we hear. In contrast, a piano produces sound through the vibration of strings, a guitar produces sound through the vibration of strings, a handbell produces sound through the vibration of metal, and a talking drum produces sound through the vibration of a stretched membrane.

**Question 5**
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Which of the following particles/rays do not originate from the nucleus of an atom?

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**Question 6**
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Soft iron is used in making the armature of an electric bell because it

**Answer Details**

Soft iron is used in making the armature of an electric bell because it loses its magnetism readily. This is due to its low coercivity, which means that it is easily magnetized and demagnetized. In an electric bell, the armature needs to be magnetized and demagnetized rapidly in order to vibrate back and forth, striking the bell and producing the sound. If the armature were made of a material that retained its magnetism for a long time, it would not vibrate back and forth as required, and the bell would not ring properly. Therefore, soft iron is an ideal material for the armature of an electric bell because it can be easily magnetized and demagnetized, allowing the bell to ring properly.

**Question 7**
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CalcuIate the power delivered by a 3-phase line if its voltage and current at 132KV and 60A respectively.

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**Question 8**
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What is the difference in the amount of heat given out by 4kg of steam and 4kg of water when both are cooled from 100oC to 80oC? (Specific latent heat of steam = 2.260,000J kg-1) (Specific heat capacity of water =4,200 J kg-1)

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**Question 9**
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The heating element in an electric kettle is usually located near the bottom of the kettle because

**Answer Details**

The heating element in an electric kettle is usually located near the bottom of the kettle because of convection currents. When the heating element is turned on, it heats up the water in contact with it. Hot water is less dense than cold water, so it rises to the top of the kettle while the colder water sinks to the bottom. This creates a convection current, where the hot water at the top of the kettle is replaced by the colder water at the bottom, which in turn is heated by the heating element. This process continues until all the water in the kettle is heated to the desired temperature. If the heating element were located near the top of the kettle, the convection current would be less efficient because the hot water at the top would not mix as easily with the colder water at the bottom. By placing the heating element near the bottom of the kettle, the convection currents are more effective at carrying the heat to all parts of the water, resulting in faster heating and more efficient energy use. Therefore, the correct answer is option (D) - the convectional currents which are set up can carry heat to all parts of the water.

**Question 10**
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The electric potential at point P in the diagram above can be expressed as

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**Question 11**
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Which of the following substances is most viscous at room temperature?

**Answer Details**

Out of the given options, palm oil is the most viscous at room temperature. Viscosity is a measure of a fluid's resistance to flow, and is affected by factors such as temperature and molecular structure of the fluid. Palm oil has a higher molecular weight and longer hydrocarbon chains compared to the other options, which leads to stronger intermolecular forces and greater resistance to flow. This makes it more viscous than water, alcohol, petrol, and kerosene at room temperature.

**Question 12**
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A string of length 1.0 m vibrates in 10 loops. If the total mass of the string is 1.0 x 10^{-3} kg and the tension in it is 10N, calculate the frequency of the vibration.

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**Question 13**
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Which of the following is used in a nuclear reactor to slow down fast-moving neutrons?

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**Question 14**
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The count rate of an alpha-particle source is 400 per minute. If the half-life of the source is 5 days, what would be the count rate per minute after 15 days?

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The count rate of an alpha-particle source refers to the number of alpha particles emitted by the source in one minute. The half-life of a radioactive source is the time it takes for half of the radioactive atoms to decay. If the count rate of the alpha-particle source is 400 per minute and the half-life of the source is 5 days, this means that after 5 days, the count rate will decrease to 200 per minute (half of 400). After another 5 days (a total of 10 days), the count rate will decrease to 100 per minute (half of 200). After another 5 days (a total of 15 days), the count rate will decrease to 50 per minute (half of 100). Therefore, the count rate per minute after 15 days will be 50, and the correct answer is option (C) 50.

**Question 15**
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The refractive index of a medium relative to air is 1.8. Calculate the critical angle for the medium to the nearest degree.

**Answer Details**

The critical angle is the angle of incidence in the medium for which the angle of refraction is 90 degrees (the refracted ray lies along the boundary). The critical angle is given by the formula `sin c = 1/n`, where `c` is the critical angle and `n` is the refractive index of the medium relative to air. Substituting `n = 1.8` into the formula, we get `sin c = 1/1.8 = 0.556`. Taking the inverse sine of both sides, we get `c = sin^{-1}(0.556)`. Evaluating this on a calculator, we get `c ≈ 34°`. Therefore, the critical angle for the medium is approximately 34 degrees. Answer is the correct answer.

**Question 16**
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Lenz's law of electromagnetic induction states that

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Lenz's law of electromagnetic induction is a fundamental law in physics that describes the relationship between the change in magnetic flux and the induced electromotive force (EMF) and current. The law states that when there is a change in the magnetic flux through a closed loop, an EMF is induced in the loop that is proportional to the rate of change of the flux. Furthermore, the direction of the induced EMF is such that it opposes the change that produced it. In other words, the induced current flows in a direction that creates a magnetic field that opposes the change in the original magnetic field. This means that if the magnetic flux through a circuit increases, the induced current will create a magnetic field that opposes the increase in flux. Similarly, if the flux through the circuit decreases, the induced current will create a magnetic field that opposes the decrease in flux. Therefore, among the given options, the correct answer is (B) the induced current in a conductor is in such a direction as to oppose the change producing it.

**Question 17**
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A wire of length 100cm and cross-sectional area of 2.0 x 10^{-3}cm^{2} has a resistance of 0.10 Ω. Calculate its electrical conductivity.

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Electrical conductivity is a measure of how easily a material can conduct electricity. It is the reciprocal of electrical resistivity. The formula for electrical conductivity is given by: σ = 1/ρ Where σ is electrical conductivity and ρ is electrical resistivity. We are given the length (L) of the wire as 100 cm, the cross-sectional area (A) as 2.0 x 10^-3 cm^2, and the resistance (R) as 0.10 Ω. We can use Ohm's law to calculate the resistivity (ρ): R = ρ*L/A ρ = RA/L Substituting the given values, we get: ρ = (0.10 Ω)*(2.0 x 10^-3 cm^2)/100 cm ρ = 2.0 x 10^-6 Ω cm Now, we can calculate the electrical conductivity using the formula: σ = 1/ρ σ = 1/(2.0 x 10^-6 Ω cm) σ = 5.0 x 10^5 Ω^-1 cm^-1 Therefore, the electrical conductivity of the wire is 5.0 x 10^5 Ω^-1 cm^-1. Answer: 5.0 x 10^5 Ω^-1 cm^-1

**Question 18**
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Which of the following is not a component of a d.c. electric motor?

**Answer Details**

The components of a DC electric motor include an armature, a commutator, field magnets, carbon brushes, and sometimes, brushes or slip rings. The armature is the rotating part of the motor that converts electrical energy into mechanical energy. The commutator is a device that changes the direction of the current flowing through the armature, ensuring that it continues to rotate in the same direction. The field magnets produce a magnetic field that interacts with the current flowing through the armature, causing it to rotate. Carbon brushes are used to transfer electrical current between stationary wires and moving parts of the motor, such as the commutator or slip rings. Slip rings are used in some types of motors as an alternative to the commutator to transfer electrical current between the stationary wires and the rotating parts of the motor. Therefore, the component that is not a component of a DC electric motor is slip rings. Although slip rings can be used in some types of electric motors, they are not commonly used in DC electric motors. Instead, DC motors typically use a commutator to transfer electrical current between the stationary wires and the rotating armature. So the correct answer to the question is "Slip rings".

**Question 19**
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Two simple pendula x and y make 400 and 500 oscillations respectively in equal time. If the period of oscillation of x is 1.5 seconds, what is the period of oscillation of y?

**Answer Details**

The number of oscillations of a pendulum in a given time depends on its period of oscillation. The period is the time taken for one complete oscillation. The relationship between the period and the number of oscillations is direct; that is, as the period of a pendulum decreases, the number of oscillations it makes in a given time increases. In this question, we are given that the period of oscillation of pendulum x is 1.5 seconds, and it makes 400 oscillations in equal time. We are also given that pendulum y makes 500 oscillations in equal time. Since both pendula are making oscillations in equal time, we can assume that the time taken for each pendulum to make one oscillation is the same. To find the period of oscillation of pendulum y, we can use the relationship between the period and the number of oscillations. If pendulum x with a period of 1.5 seconds makes 400 oscillations in equal time, then the total time taken for 400 oscillations is: Time taken by pendulum x = 400 x 1.5 seconds = 600 seconds Since pendulum y makes 500 oscillations in the same time, the period of oscillation of y can be calculated as follows: Time taken by pendulum y for 500 oscillations = 600 seconds Period of pendulum y = Total time taken / Number of oscillations Period of pendulum y = 600 seconds / 500 oscillations Period of pendulum y = 1.2 seconds Therefore, the period of oscillation of pendulum y is 1.2 seconds.

**Question 20**
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The magnitude of the force required to make an object of mass M move with speed V in a circular path of radius R is given by the expression.

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The magnitude of the force required to make an object of mass M move with speed V in a circular path of radius R is given by the expression mv²/r. This is known as the centripetal force. When an object moves in a circle, it experiences a change in direction which means it is accelerating. Since there is acceleration, there must be a force acting on the object. The centripetal force is the force that acts on an object moving in a circular path, directed towards the center of the circle, and is necessary to keep the object moving in a circular path. The magnitude of this force is directly proportional to the mass of the object, the square of its velocity and inversely proportional to the radius of the circular path. Thus, the correct option is (C) mv²/r.

**Question 21**
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A rocket is launched from the surface of the earth. If the radius of the earth is 6.4 x 10^{6}m and the acceleration of free fall due to gravity is 1Oms^{-1} calculate the escape velocity of the rocket.

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**Question 22**
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Which of the following is not part of the electromagnetic spectrum?

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The correct answer is "Alpha particle". Alpha particles are not part of the electromagnetic spectrum. Alpha particles are actually helium-4 nuclei, consisting of two protons and two neutrons, and they are emitted by some types of radioactive decay. The other options are all part of the electromagnetic spectrum. The electromagnetic spectrum includes radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. They are all forms of electromagnetic radiation characterized by different wavelengths and frequencies.

**Question 25**
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A platinum-resistance thermometer has a resistance of 5Ω at 0°C and 9Ω at l00°C. Assuming that resistance changes uniformly with temperature, calculate the resistance of the thermometer when the temperature is 45°C.

**Answer Details**

A platinum-resistance thermometer has a resistance of 5 Ω at 0°C and 9 Ω at 100°C, and it is assumed that resistance changes uniformly with temperature. We need to calculate the resistance of the thermometer when the temperature is 45°C. We can start by finding the change in resistance as the temperature changes from 0°C to 100°C: ΔR = 9 Ω - 5 Ω = 4 Ω This change occurs over a temperature range of 100°C - 0°C = 100°C, so the resistance changes by 4 Ω per 100°C. To find the resistance at 45°C, we can use the following proportion: (ΔR / ΔT) = (R₂ - R₁) / (T₂ - T₁) Where: ΔR = change in resistance ΔT = change in temperature R₁ = initial resistance (at 0°C) R₂ = final resistance (at 45°C) T₁ = initial temperature (0°C) T₂ = final temperature (45°C) Substituting the known values, we get: (4 Ω / 100°C) = (R₂ - 5 Ω) / (45°C - 0°C) Simplifying the equation: R₂ - 5 Ω = (4 Ω / 100°C) x 45°C R₂ - 5 Ω = 1.8 Ω R₂ = 6.8 Ω Therefore, the resistance of the platinum-resistance thermometer at 45°C is 6.8 Ω. Answer: 6.8 Ω.

**Question 26**
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A ball of mass 5.0kg hits a smooth vertical wall normally with a speed of 2ms^{-1} and rebounds with the same speed. Determine the impulse experienced by the ball

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The impulse experienced by the ball can be calculated using the impulse-momentum theorem, which states that the impulse on an object is equal to the change in momentum of the object. In this case, the ball has an initial momentum of p = mv, where m is its mass and v is its velocity, and it rebounds with the same speed, but in the opposite direction. This means that the final momentum of the ball is -mv. The change in momentum, therefore, is: Δp = -mv - mv = -2mv The impulse experienced by the ball is equal to the change in momentum, so: impulse = Δp = -2mv Substituting the given values, we get: impulse = -2(5.0 kg)(2 m/s) = -20.0 kg m/s Since impulse is a vector quantity, its magnitude is always positive. Therefore, we take the absolute value of the calculated impulse to get: impulse = 20.0 kg m/s So the correct answer to the question is 20.0 kg m/s.

**Question 27**
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Two spanners X and Y of lengths 15cm and 20cm respectively are used in turn to give a screw of pitch 2mm one complete rotation. If Rx and Ry are the respective velocity ratios of the spanners then the ratio Rx : Ry is

**Question 28**
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A boy walks away from a plane mirror at a speed of 3 ms-1 in a direction normal to the surface of the mirror. At what speed is his image approaching him?

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**Question 29**
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When a ray of light is incident normally on an air- glass interface, its angle of refraction is

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When a ray of light is incident normally on an air-glass interface, its angle of refraction is 0 degrees. This is because when light travels from one medium to another, it changes direction, a phenomenon known as refraction. The amount of refraction depends on the angle at which the light enters the second medium, as well as the properties of the two media, such as their refractive indices. In the case of an air-glass interface, since the angle of incidence is normal, that is, the ray of light is perpendicular to the surface, the angle of refraction is also zero. This means that the light continues to travel in a straight line without changing its direction. So the correct answer to the question is 0 degrees.

**Question 30**
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Which of the following is used in a nuclear reactor to slow down fast-moving neutrons?

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In a nuclear reactor, a chain reaction is sustained by the collision of neutrons with atomic nuclei, which leads to the release of more neutrons and a large amount of energy. However, not all neutrons are capable of causing this chain reaction, as only neutrons with sufficient energy (known as fast neutrons) can interact with the nuclei to cause the chain reaction. To increase the efficiency of the chain reaction, it is desirable to slow down these fast-moving neutrons so that they are more likely to interact with atomic nuclei and cause the chain reaction to continue. This is achieved by using a material known as a moderator, which is placed in the reactor core to slow down the fast neutrons. Of the options given, the material commonly used as a moderator in nuclear reactors is graphite rods. Graphite is made of carbon atoms and has a layered structure that allows it to efficiently slow down fast neutrons. Other materials such as heavy water and beryllium can also be used as moderators, but graphite is the most commonly used. Therefore, the correct answer to the question is "Graphite rods".

**Question 31**
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The main function of the mouth of a telephone is to convert sound energy into

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The main function of the mouth of a telephone is to convert sound energy into electrical energy. When a person speaks into the mouthpiece of a telephone, the sound waves from their voice cause a diaphragm inside the microphone to vibrate. This vibration is then converted into an electrical signal, which is transmitted through the telephone wires to the receiver at the other end. The receiver then converts the electrical signal back into sound waves, which can be heard by the person on the other end of the line. Therefore, the mouth of a telephone does not convert sound energy into heat, light, chemical, or mechanical energy, but rather into electrical energy.

**Question 32**
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The linear expansivity of a metal P is twice that of another metal Q. When these materials are heated through the same temperature change, their increase in length is the same. Calculate the ratio of the original length of P to that of Q.

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Let the original length of metal P be x and the original length of metal Q be y. We know that the increase in length is given by: ΔL = L₀αΔθ where ΔL is the increase in length, L₀ is the original length, α is the coefficient of linear expansion, and Δθ is the change in temperature. Since the increase in length is the same for both metals, we can write: ΔL_{P} = ΔL_{Q} L_{P}α_{P}Δθ = L_{Q}α_{Q}Δθ L_{P}/L_{Q} = α_{Q}/α_{P} Since we are told that the linear expansivity of P is twice that of Q, we can write: α_{P} = 2α_{Q} Substituting into the equation above, we get: L_{P}/L_{Q} = α_{Q}/2α_{Q} = 1/2 Therefore, the ratio of the original length of P to that of Q is 1:2. Answer: 1:2

**Question 33**
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A body of mass 4.2kg moving with velocity 10ms^{-1} due east, hits a stationary body of mass 2.8kg. If they stick together after collision and move with velocity V due east, calculate the value of V

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In this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it. The initial momentum of the system before the collision is given by: p1 = m1 * v1 where m1 is the mass of the first body (4.2 kg) and v1 is its velocity (10 m/s). p1 = 4.2 kg * 10 m/s p1 = 42 kg m/s The second body is stationary, so its initial momentum is zero: p2 = 0 kg m/s The total initial momentum of the system is therefore: p_initial = p1 + p2 p_initial = 42 kg m/s After the collision, the two bodies stick together and move with a common velocity V. The total mass of the system is the sum of the masses of the two bodies: m_total = m1 + m2 m_total = 4.2 kg + 2.8 kg m_total = 7 kg The final momentum of the system is: p_final = m_total * V According to the principle of conservation of momentum, the total initial momentum of the system is equal to the total final momentum of the system: p_initial = p_final Substituting the values we have found, we get: 42 kg m/s = 7 kg * V Solving for V, we get: V = 42 kg m/s / 7 kg V = 6 m/s Therefore, the value of V after the collision is 6 m/s due east. Thus, the correct answer is "6ms^-1".

**Question 34**
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The inside of a vacuum flask is usually coated with silver to reduce heat lost by

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The inside of a vacuum flask is usually coated with silver to reduce heat lost by radiation. Heat can transfer from one object to another through convection, conduction, and radiation. In a vacuum flask, there is a vacuum between the two walls of the flask which minimizes heat loss by convection and conduction. However, heat can still be transferred by radiation, which is the emission of electromagnetic waves from a body. The silver coating on the inner wall of the vacuum flask reflects the heat radiation back into the flask, reducing the amount of heat lost to the surroundings. Therefore, silver is used to minimize heat loss by radiation in a vacuum flask.

**Question 35**
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The diagram above represents a portion of a micrometer screw gauge in which the horizontal scale is in millimetres. What is the reading on the instrument?

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**Question 36**
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The velocity ratio and efficiency of a system of pulleys are 6 and 80% respectively. How much effort is required to lift a load of mass 120kg with this system? (g=10ms^{-2})

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**Question 37**
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ln the diagram above, the resistor has a resistance 8 ? while the reactances of the inductor and the capacitor are 10 ? and 16 ? respectively Calculate the current in the circuit

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**Question 38**
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A cell of e.m.f. 1.5V is connected in series with a resistor of resistance 39. A high-resistance voltmeter connected across the cell registers only 0.9V. Calculate the internal resistance of the cell

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**Question 39**
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The resistance in a series R-C circuit is 5 Ω. If the impedance of the circuit is 13 Ω, calculate the reactance of the capacitor

**Answer Details**

In a series R-C circuit, the total impedance is given by: Z = √(R^2 + Xc^2) where R is the resistance and Xc is the reactance of the capacitor. Since the impedance of the circuit is 13 Ω and the resistance is 5 Ω, we have: 13 = √(5^2 + Xc^2) Squaring both sides, we get: 169 = 25 + Xc^2 Simplifying, we get: Xc^2 = 144 Taking the square root of both sides, we get: Xc = ±12 Since we are looking for the magnitude of the reactance, we take the positive value: Xc = 12 Ω Therefore, the reactance of the capacitor is 12 Ω.

**Question 40**
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The main reason why rice cooks faster in a pressure cooker than in cooking pot is that

**Answer Details**

The main reason why rice cooks faster in a pressure cooker than in a cooking pot is that the boiling point of water in the cooker is raised. In a pressure cooker, water boils at a higher temperature due to the increased pressure inside the cooker. This increase in temperature means that the rice cooks faster as it is exposed to higher temperatures than it would be in a cooking pot. Additionally, less heat escapes from the cooker, and the vapour pressure in the cooker is constant, contributing to the rice cooking faster.

**Question 41**
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The diagram above illustrates a variation of the displacement y of a wave particle with time t. lf the velocity of wave is 250ms^{-1}, calculate the distance between two successive particles which are in phase

**Question 42**
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The walls and ceilings of many standard auditoria are covered with perforated pads to

**Answer Details**

The perforated pads on the walls and ceilings of standard auditoria are there to reduce the effect of reverberations of sound waves. When sound waves are produced in a room, they bounce off the walls, floor, and ceiling, creating an echo-like effect that can make it difficult to hear and understand speech or music clearly. The perforations in the pads allow sound waves to pass through them and get absorbed by a layer of sound-absorbing material behind them. This reduces the amount of sound waves bouncing around the room, leading to clearer and more intelligible sound. The pads do not increase the intensity or loudness of sound waves, nor do they increase the interference effect or decrease the frequency of sound waves.

**Question 43**
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A sound wave of velocity 350 ms^{-1} is directed towards the surface of water. lf the ratio of the wavelength of sound in water to that in air is 425:100, calculate the velocity on the wave in water

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The velocity of a sound wave depends on the properties of the medium through which it is traveling. The formula for the velocity of a sound wave is: v = λf where v is the velocity, λ is the wavelength, and f is the frequency of the wave. In this question, we are given that the velocity of sound in air is 350 ms^-1 and the ratio of the wavelength of sound in water to that in air is 425:100. Let's assume that the frequency of the wave remains constant as it passes from air into water. If the wavelength of the sound wave in air is λ_{air}, then the wavelength of the same wave in water is: λ_{water} = (425/100)λ_{air} = 4.25λ_{air} Now we can use the formula for the velocity of a sound wave to find the velocity of the wave in water: v_{water} = λ_{water}f Since the frequency of the wave remains constant, we can write: v_{water} = (4.25λ_{air})f We know that the velocity of the wave in air is 350 ms^-1, and we can write: v_{air} = λ_{air}f Solving for f, we get: f = v_{air}/λ_{air} Substituting this expression for f into the previous equation, we get: v_{water} = (4.25λ_{air})v_{air}/λ_{air} Simplifying, we get: v_{water} = 4.25v_{air} Substituting the given value for the velocity of sound in air, we get: v_{water} = 4.25 x 350 ms^-1 Simplifying, we get: v_{water} = 1487.5 ms^-1 Therefore, the velocity of the wave in water is 1487.5 ms^-1. Option (D) is the correct answer.

**Question 44**
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What is the decay constant of a radioactive element whose half-life is 3 seconds

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The decay constant (λ) is a measure of the probability that a radioactive nucleus will decay per unit time. It is related to the half-life (t_{1/2}) of the radioactive element by the equation: λ = ln(2) / t_{1/2} where ln(2) is the natural logarithm of 2, which is approximately 0.693. Substituting the given half-life of 3 seconds into the equation, we have: λ = ln(2) / 3 s λ ≈ 0.231s^{-1} Therefore, the decay constant of the radioactive element is approximately 0.231s^{-1}. The option closest to this value is 0.23s^{-1}.

**Question 45**
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Calculate the amount of heat generated in an external load of resistance 89 if an alternating current of peak value 5A is passed through for 100s.

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**Question 47**
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When a ray of light is incident normally on an air- glass interface, its angle of refraction is

**Question 48**
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A converging lens of focal length 5cm forms a virtual image which is 10cm from the lens. How far from the lens is the object?

**Question 49**
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A loaded test-tube which floats upright in water is carefully and slightly depressed and then released. Which of the following best describes the sub-sequent motion of the test-tube?

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When the loaded test-tube is depressed and then released, it experiences a restoring force that brings it back to its original position. This restoring force arises from the displaced water that exerts an upward buoyant force on the test-tube. Since the restoring force acts in the opposite direction to the displacement, the motion of the test-tube is oscillatory, with the test-tube moving back and forth around its equilibrium position. Therefore, the correct answer to the question is "Oscillatory".

**Question 50**
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The diagram above illustrates an isolated metal sphere carrying charge W in a medium whose permittivity is so. The magnitude of the electric field intensity at P can be expressed as

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The electric field intensity at point P due to the isolated charged sphere is given by Coulomb's law, which states that the magnitude of the electric field intensity is directly proportional to the charge on the sphere and inversely proportional to the square of the distance between the sphere and point P. Mathematically, it is expressed as: E = Q/(4πε_{o}r^{2}) where E is the electric field intensity, Q is the charge on the sphere, ε_{o} is the permittivity of the medium, and r is the distance between the sphere and point P. Therefore, the correct option is (b) Q/(4πε_{o}r^{2}).

**Question 51**
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A ray of light strikes a plane mirror at a glancing angle of 50^{o}. Calculate the angle between the incident and reflected rays

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**Question 52**
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A ray of light is incident on a glass block as shown in the diagram above. If the reflected and the retracted rays are perpendicular to each other, what is the refractive index of the glass relative to air.?

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**Question 53**
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The diagram above illustrates the velocity-time graph of the motion of a body. Calculate the total distance covered by the body

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**Question 54**
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The distance between two successive crests of a water is 1m. lf a particle on the surface of the water makes two complete vertical oscillations in 1 second, calculate the speed of the wave

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The distance between two successive crests of a wave is called its wavelength, denoted by λ. In this question, the wavelength is given as 1m. The number of complete oscillations (or cycles) of a particle on the surface of the water in 1 second is called the frequency, denoted by f. In this question, the frequency is given as 2 cycles per second (or 2 Hz). The speed of a wave is given by the formula: v = f × λ Substituting the given values, we get: v = 2 Hz × 1m v = 2 m/s Therefore, the speed of the wave is 2 m/s. The correct answer is option (C) 2.0 ms^-1.

**Question 55**
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The diagram above represents a stationary wave set up in a string which is fixed at both ends. lf the frequency of the wave is 256Hz and the distance N1 N2 equals 1.5m, calculate the speed of the wave.

**Answer Details**

The speed of a wave can be calculated using the formula: speed = frequency x wavelength In a stationary wave, the distance between two consecutive nodes (or antinodes) represents half of the wavelength. Therefore, the wavelength of the wave in the given diagram can be calculated as: wavelength = 2 x distance(N1N2) = 2 x 1.5m = 3m Given that the frequency of the wave is 256Hz, we can now calculate its speed: speed = frequency x wavelength = 256Hz x 3m = 768ms^-1 Therefore, the speed of the wave is 768ms^{-1}.

**Question 56**
**Report**

The diagram above illustrates the conversion of a galvanometer of resistance 29 to an ammeter. The galvanometer gives a full-scale deflection for a current of 10mA. Calculate the value of R.