Sand is being dropped from a stationary dropper at a rate of $0.5 \mathrm{kgs}^{-1}$ on a conveyor belt moving with a velocity of $5 \mathrm{~ms}^{-1}$. The power needed to keep belt moving with the same velocity will be :

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Conservation of Momentum

Sand is being dropped from a stationary dropper at a rate of

0.5 kgs^{- 1}

on a conveyor belt moving with a velocity of

5 ms^{- 1}

. The power needed to keep belt moving with the same velocity will be :

(A)1.25 W
(B)2.5 W
(C)6.25 W
(D)12.5 W✓ Correct

Answer: (D)

Solution

The thrust force on the belt is

F = λ v_{rel}

, where

λ = 0.5

kg/s is the mass rate and

v_{rel} = 5

m/s. Thus

F = 0.5 \times 5 = 2.5

N. The power required is

P = F \times v = 2.5 \times 5 = 12.5

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option

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