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A balloon having mass m is filled with gas and is held in hands of a boy. Then suddenly it get released and gas starts coming out of it with a constant rate. The velocity of the ejected gases is also constant $2 m s^{- 1}$ with respect to the balloon. Find out the velocity of the balloon, in $m s^{- 1}$ , when the mass of gas is reduced to half. Take ln(2) = 0.7

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answer is 1.4.

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Detailed Solution

Since gases are ejected out during motion we use

$\int_{0}^{v} mdv = \int_{m_{0}}^{m_{0} / 2} udm$

$\Rightarrow v = u l n 2 = 2 l n (2) {ms}^{- 1} \approx 1.4 {ms}^{- 1}$

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