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A stationary rocket of total initial mass $m_{0}$ is expelling exhaust gas at a steady speed $v_{e}$ with respect to itself. There is no external force on rocket. When its mass is reduced to $m_{0} / 2$ , the velocity attained by the rocket will be

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$0.5 v_{e}$

$0.69 v_{e}$

$2 v_{e}$

$v_{e}$

answer is C.

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Detailed Solution

$m Δ \vec{v} = Δ m {\vec{v}}_{rel} \Rightarrow \int_{0}^{v} dv = - v_{e} \int_{m_{0}}^{m_{0} / 2} \frac{dm}{m} \Rightarrow v = v_{e} (In 2)$

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