A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of $1 \mathrm{~kg~s}^{-1}$ and at a speed of $10 \mathrm{~ms}^{-1}$. Then, the initial acceleration of the block, in $\mathrm{ms}^{-2}$, will be:

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Conservation of Momentum

A block of metal weighing 2 kg is resting on a frictionless plane (as shown in figure). It is struck by a jet releasing water at a rate of

1 kg s^{- 1}

and at a speed of

10 ms^{- 1}

. Then, the initial acceleration of the block, in

ms^{- 2}

, will be:

(A)3
(B)6
(C)5✓ Correct
(D)4

Answer: (C)

Solution

The force exerted by the water jet is

F = v \frac{d m}{d t} = 10 \times 1 = 10

N. Using Newton's second law for the block:

F = M a

, so

10 = 2 a

, giving

a = 5

m/s².

JEE Main · 2022 · 29 Jun 2022 · Shift 1 · Single correct option

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