Sand is being dropped from a stationary dropper at a rate of 0 . 5   kg   s - 1 on a conveyor belt…

When the sand is dropped on the conveyor belt its velocity will become equal to that of the conveyor. Therefore, $v=5 \mathrm{m} {\mathrm{s}}^{-1}$.

The force required to keep the conveyor belt moving will be equal to the gain in the momentum by the sand per second.

$$\begin{gathered} \Rightarrow F=\frac{dm}{dt}v \\ \Rightarrow F=0.5\times 5=2.5 \mathrm{N} \end{gathered}$$

Now the power required to keep the conveyor belt moving will be,

$$\begin{gathered} P=Fv \\ \Rightarrow P=2.5\times 5=12.5 \mathrm{W}. \end{gathered}$$