Work-energy-power practice · Medium

None is correct because the potential energy is proportional to the square of the stretch, and stretching it 5 times more (from 2mm to 10mm) will result in 25 times more potential energy, which is 100J.

Option A (Work done by the boy against the gravitational force acting on the block) is correct because the gain in gravitational potential energy is equal to the work done against gravity.

Option A (Top of the circle) is correct because the tension is minimum at the top of the circle for a constant speed.

Option A (If both Assertion and Reason are true and Reason is correct explanation of Assertion) is correct because the potential energy of a spring indeed varies parabolically with extension or compression, and this is because the potential energy is proportional to the square of the extension or compression.

Option A (1) is correct because the coefficient of restitution for a perfectly elastic collision is 1, indicating no energy loss.

Option A (Only momentum is conserved) is correct because, by definition, in an inelastic collision, kinetic energy is not conserved, but momentum is always conserved.

The correct answer is A (2 Mgr) because the difference in kinetic energy is equal to the difference in potential energy.

Option A (If both Assertion and Reason are true and Reason is correct explanation of Assertion) is correct because the Work-Energy Theorem states that the net work done on a particle equals its change in kinetic energy, and this applies directly to a single-particle system.

Option C (${n^2}U$) is correct because the potential energy is proportional to the square of the extension, so increasing the extension by a factor of 'n' increases the potential energy by a factor of n squared.

Option A (Statement-I & II are true) is correct because engine B does the same work in less time, hence has more power, and power is indeed the dot product of force and velocity.

Option A is correct because in uniform circular motion, the force (tension in the string) is always perpendicular to the displacement, so no work is done.

Option B (31.4 m/s) is correct because average speed is total distance divided by total time, and for constant speed, it equals the speed itself.

Option D is correct because in a circular path with constant velocity, the net work done is zero as there is no change in kinetic energy.

Option D (All of the above) is correct. Since KE is the same, and the retarding force is the same, the work done to stop them is the same, hence the distance is the same. Also, momentum depends on mass, and time to stop depends on mass.

Option C ($K/2$) is correct because at the highest point, the vertical velocity is zero, and only the horizontal component of the initial velocity remains, which is $v_0 \cos(45^\circ) = v_0/\sqrt{2}$. The kinetic energy at the highest point is therefore $K/2$.

Option A (Is four times the velocity at any moment) is correct because the rate of change of kinetic energy is equal to the power, which is force times velocity, and the force is related to the acceleration.

Option C ($\frac{1}{{40}}\mathrm{m}{\mathrm{s}^{ - 2}}$) is correct because the acceleration is calculated by dividing the force exerted by the bullets on the car by the mass of the car.

Option C (Joule-metre) is correct because the potential energy U has units of Joules, and the expression Kx/(x²⁺a²) must also have units of Joules. Therefore, K must have units of Joule-meter.

Option D (Both (2) and (3) are correct) is correct because the magnitude of momentum is conserved, and the mechanical energy of the system remains constant as there are no external forces.

Option A ($m\mathrm{g}\left( {\frac{h}{x} + 1} \right)$) is correct because it is derived from the work-energy theorem, considering both the gravitational potential energy and the work done by the sand.

Option B (121 J) is correct because the work done is the dot product of the force and displacement vectors.

Option D (Statement-1 is false, Statement- 2 is true) is correct. Kinetic energy depends on the frame of reference, so Statement-1 is false, and Statement-2 correctly states that kinetic energy varies with different frames of reference.

Option B is correct because with the same displacement, a stiffer spring (A) requires more work, and with the same force, a less stiff spring (B) stretches more, requiring more work.

Option C (3 mg) is correct because at the mean position, the tension in the string is the sum of the weight and the centripetal force.

The correct answer is A. One kilowatt-hour (kWh) is a unit of energy, specifically the energy consumed by a 1 kW device operating for 1 hour.

The correct answer is B. The energy required to lift the box to the same height is the same, regardless of the time taken, as energy depends on force and displacement, not time.

Option B (When the mass is the lowest point of the circle) is correct because the tension in the wire is greatest at the bottom due to the combined effect of the weight of the mass and the centripetal force required for circular motion.

Option A ($m\mathrm{g}\left( {l - h} \right)$) is correct because the man's potential energy increases by the difference between the ladder length and the balloon's descent.