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  4. Sand is being dropped on a conveyer belt at the rate of M kg/s. The force necessary to keep the belt moving with a constant velocity of v m/s will be

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Q. Sand is being dropped on a conveyer belt at the rate of $M\, kg/s$. The force necessary to keep the belt moving with a constant velocity of v m/s will be

AIPMTAIPMT 2008Laws of Motion

Solution:

$F=\frac{d}{d t}(M v)=v \frac{d M}{d t}+M \frac{d v}{d t}$
As $v$ is a constant,
$F=v \frac{d M}{d t} . $
But $\frac{d M}{d t}=M kg / s$
$\therefore$ To keep the conveyer belt moving at $v m / s$, force needed $=v M$ newton.