A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 $ms^{−1}$, the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is

A 600 kg rocket is set for a vertical firing. If the exhaust speed is 1000 $ms^{−1}$, the mass of the gas ejected per second to supply the thrust needed to overcome the weight of rocket is 

(a) 117.6 $kg \;s^{−1}$

(b) 58.6 $kg \;s^{−1}$

(c) 6 $kg \;s^{−1}$

(d) 76.4 $kg \;s^{−1}$

[NEET 1990]

\[ \sum F = ma \] \[ F_{\text{thrust}} - mg = ma\]

Thrust needed to overcome the weight, so $F_{thrust} =mg$ This means $a=0$

Fuel Mass Flow rate, $\frac{m}{t}=\dot{m}$ Initial velocity, $u=0$

\[ \frac{mv - mu}{t} = mg \] \[ \dot{m} v = mg \] \[ \dot{m} \hspace{2mm}1000 = 600 \cdot 10 \] \[ \dot{m} = 6\ \text{kg/s} \]