Work-energy-power practice · Mixed difficulty

Option A (0.41) is correct because it is calculated by finding the tangential acceleration and then dividing by the radius to find the angular acceleration.

Option D ($\frac{-1}{4} K x^2$) is correct because the work done by the spring force on each block is half of the total work done by the spring, and the spring force does negative work.

Option B (Same) is correct because the energy required to raise the box to the same height is the same, regardless of the time taken.

Option D ($164 {~J}$) is correct because it's the result of integrating the force function over the given displacement.

Option A ($1: 2$) is correct because it is the ratio of linear momenta calculated from the given masses and the condition of equal kinetic energies.

Option A (25) is correct because the percentage of potential energy lost is calculated by finding the difference in potential energy and dividing by the initial potential energy.

Option D (3 U) is correct because the potential energy stored in a spring is proportional to the square of the compression, and the increase in potential energy is calculated accordingly.

Option A (50%) is correct because the percentage increase in momentum is calculated based on the increase in kinetic energy using the relationship between KE and momentum.

Option A (The momentum of a body by both observers may be same) is correct because if both observers are at rest relative to each other, the momentum of a body they measure can be the same.

Option A (normal acceleration) is correct because uniform circular motion involves acceleration directed towards the center.

Option D ($7.07\,\mathrm{m}{\mathrm{s}^{ - 2}}$) is correct because the maximum speed is calculated using the centripetal force formula and the breaking tension of the string.

Option A (If both Assertion & reason are True & the Reason is a correct explanation of the Assertion) is correct because centripetal force is always perpendicular to the displacement, hence the work done is zero.

Option C (Acceleration) is correct because a body in equilibrium has a net force of zero, which implies zero acceleration according to Newton's first law.

Option C (If two protons are brought towards each other the PE of the system decreases) is wrong because bringing two protons closer increases the potential energy due to electrostatic repulsion.

Option C is correct because the velocity exchange only happens when the masses are equal, ensuring momentum and kinetic energy are conserved in the specific way described.

Option B is correct because if both speed and radius are doubled, the centripetal force doubles, but the statement that centripetal force is directly proportional to speed is false.

Option D (None of the above) is technically more accurate, since the work done by a conservative force is the *negative* of the change in potential energy, or the *negative* change in potential energy of the system.

Option A is correct because the law of conservation of momentum is indeed a consequence of Newton's III law, and action-reaction pairs are internal forces in collisions, providing the necessary framework for momentum conservation.

Option A ($\mathrm{P}=\mathrm{dK} / \mathrm{dv}$) is incorrect. Option B ($\mathrm{P}=\mathrm{dK} / \mathrm{dt}$) is also incorrect. The correct answer is not among the options provided. However, if we consider the relation between Kinetic Energy (K) and momentum (P), we have $K = \frac{{P^2}}{{2m}}$. Therefore, $P = \sqrt{{2mK}}$. Differentiating K with respect to v, we get $\frac{{dK}}{{dv}} = mv = P$. So, the closest correct answer would be A, but it should be $\frac{{dK}}{{dv}} = P$.

Option C is correct because a force is indeed needed to maintain uniform circular motion due to the constant change in direction (centripetal acceleration), but the reason is false because acceleration is not zero in uniform circular motion.

Option B is correct because energy conservation is a fundamental principle, but kinetic energy conservation is specific to elastic collisions.

Option D (Both A and B are false) is correct because energy is conserved in the ball bouncing scenario (though converted to other forms), and acceleration in uniform circular motion is not constant due to changing direction.

Option A (400 J) is correct because the work done is equal to the change in kinetic energy, calculated using the velocities at the initial and final times.

Option C ($\frac{\pi a^2 \mu_0 I}{2 b} \omega \sin \omega t$) is correct because it represents the induced emf in the smaller loop as a function of time, considering the changing magnetic flux due to rotation.

Option A ($\mathrm{10m}{\mathrm{s}^{ - 1}},\,15m{s^{ - 1}}$) is correct because in a perfectly elastic collision with identical masses, the velocities are exchanged.