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

\frac{M v}{2} N

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Zero

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M v N

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2 M v N

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Solution

The correct option is C $M v N$
According to Newton’s second law, force is equal to rate of change of momentum.

$F = \frac{d p}{d t} = \frac{d}{d t} (m v)$

$\Rightarrow F = m \frac{d v}{d t} + v \frac{d m}{d t}$
(using product rule)

$\Rightarrow F = v \frac{d m}{d t} = M v N$ is the force required.

(because velocity is constant)

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