Physics - W.E.P. Question with Solution | TestHub

Let the initial state be $i$ (block at rest at height $h$) and the final state be $f$ (block at rest on horizontal surface). The initial kinetic energy $K{E}_i=0$ and final kinetic energy $K{E}_f=0$. The initial potential energy $P{E}_i=mgh$ and final potential energy $P{E}_f=0$. According to the Work-Energy Theorem, the net work done by all forces is equal to the change in kinetic energy: $W_{net}=\Delta KE=K{E}_f-K{E}_i=0-0=0$. The net work done consists of work done by gravity ($W_g$), work done by normal force ($W_N$), and work done by friction ($W_f$). Since the normal force is always perpendicular to displacement, $W_N=0$. So, $W_g+W_f=0$. The work done by gravity is $W_g=P{E}_i-P{E}_f=mgh-0=mgh$. Therefore, $mgh+W_f=0$, which implies $W_f=-mgh$. The magnitude of the work done by friction is $|W_f|=mgh$, which is equal to the initial gravitational potential energy. Thus, Assertion (A) is true. Reason (R) is the correct statement of the Work-Energy Theorem and directly explains why the total work done by friction must balance the work done by gravity (or initial potential energy change) to make the net work zero, given the zero change in kinetic energy.