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(C) The observer $B$ is on the ground (inertial frame). For observer $B$,the block starts from rest and moves downward with an acceleration $a$. The d

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$\frac{1}{2}mgat_0^2$

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(C) The observer $B$ is on the ground (inertial frame). For observer $B$,the block starts from rest and moves downward with an acceleration $a$. The displacement $s$ of the block in time $t_0$ is given by the equation of motion: $s = ut + \frac{1}{2}at^2$. Since initial velocity $u = 0$,the displacement is $s = \frac{1}{2}at_0^2$ (downward). The force of gravity acting on the block is $F_g = mg$ (downward). Since both the force and the displacement are in the downward direction,the work done by gravity is positive. Work done $W = F_g \cdot s = (mg) \cdot (\frac{1}{2}at_0^2) = \frac{1}{2}mgat_0^2$.

$A$ block of mass $m$ is kept in an elevator which starts moving downward with an acceleration $a$ as shown in the figure. The block is observed by two observers $A$ and $B$ for a time interval $t_0$. The observer $B$ (who is on the ground) finds that the work done by gravity on the block is:

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