A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity $4.5 \mathrm{~cm} / \mathrm{s}$. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Conservation of Momentum

A balloon has mass of 10 g in air. The air escapes from the balloon at a uniform rate with velocity

4.5 cm / s

. If the balloon shrinks in 5 s completely. Then, the average force acting on that balloon will be (in dyne).

(A)3
(B)9✓ Correct
(C)12
(D)18

Answer: (B)

Solution

The thrust force on the balloon is

F = \frac{d m}{d t} v

, where

\frac{d m}{d t} = \frac{10 g}{5 s} = 2

g/s and

v = 4.5

cm/s. Thus

F = 2 \times 4.5 = 9

g·cm/s² = 9 dyne.

JEE Main · 2022 · 28 Jul 2022 · Shift 1 · Single correct option

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