Sand is being dropped on a conveyor 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

Correct answer: (A) M v newton. Force required, F =(d(m v))/(d t) =v ((d m)/(d t) )=v M as velocity v is constant, hence F=M v newton

Q120 / 200 · NEET 2008 (Screening) · Physics

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

Correct answer
A
$M v$ newton
B
$2 M v$ newton
C
$\frac{M v}{2}$ newton
D
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 $F=M v \text { newton }$

Hence, the correct answer is option: 'A'.

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