Sand is being dropped on a conveyor belt at the rate of $M \mathrm{~kg} / \mathrm{s}$. The force necessary…

Sand is being dropped on a conveyor belt at the rate of $M \mathrm{~kg} / \mathrm{s}$. The force necessary to keep the belt moving with a constant velocity of $v \mathrm{~m} / \mathrm{s}$ will be
  1. $M v$ newton
  2. $2 M v$ newton
  3. $\frac{M v}{2}$ newton
  4. zero

Solution

Force required,
$\begin{aligned}
F & =\frac{d(m v)}{d t} \\
& =v\left(\frac{d m}{d t}\right)=v M
\end{aligned}$
as velocity $v$ is constant, hence
$F=M v \text { newton }$

Asked in: NEET 2008 (Screening)

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