Q116 / 150 · MHT CET 2025 (21 Apr Shift 2) · Physics

A conveyor belt is moving with constant velocity (V). Sand is being dropped on the belt at the rate of $\mathrm{M} \mathrm{~kg} / \mathrm{s}$. The force necessary to keep the belt moving with a constant velocity $\mathrm{V} \mathrm{m} / \mathrm{s}$ will be

  • A
    $\frac{\mathrm{MV}}{2} \mathrm{~N}$
  • B
    2 MV N
  • C
    Zero N
  • Correct answer
    D
    MV N

Solution

The sand is deposited with zero initial horizontal velocity onto the belt moving at constant velocity $V$. The force needed to maintain constant belt velocity arises solely from accelerating each infinitesimal mass $dm$ to speed $V$.

The rate of mass deposition is $M = \frac{dm}{dt}$, and the change in momentum for mass $dm$ is $dP = (dm) V$.

By Newton's second law, the required force equals the rate of momentum transfer: $F = \frac{dP}{dt} = V \frac{dm}{dt}$.

Substituting the mass flow rate gives $F = M V$.

The force necessary to maintain constant belt velocity is $MV$ N, corresponding to option D.

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

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