Laws Of Motion Ques 1
1. A $5000 $ $\mathrm{kg}$ rocket is set for vertical firing. The exhaust speed is $800 $ $\mathrm{ms}^{-1}$. To give an initial upward acceleration of $20 $ $\mathrm{ms}^{-2}$, the amount of gas ejected per second to supply the needed thrust will be $\left(g=10 \mathrm{ms}^{-2}\right)$
[1998]
(a) $127.5 $ $\mathrm{kg}$ $ \mathrm{s}^{-1}$
(b) $187.5 $ $\mathrm{kg} $ $\mathrm{s}^{-1}$
(c) $185.5 $ $\mathrm{kg} $ $\mathrm{s}^{-1}$
(d) $137.5 $ $\mathrm{kg} $ $\mathrm{s}^{-1}$
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Answer:
Correct Answer: 1.(b)
Solution: (b) Given : Mass of rocket $(\mathrm{m})=5000 $ $\mathrm{kg}$
Exhaust speed $(v)=800 $ $\mathrm{m} / \mathrm{s}$
Acceleration of rocket $(a)=20$ $ \mathrm{m} / \mathrm{s}^2$
Gravitational acceleration $(g)=10 $ $\mathrm{m} / \mathrm{s}^2$
Thrust, $\Rightarrow \frac{v d m}{d t}$
We know that upward force,
$ \begin{gathered} F=m(g+a)-5000(10+20) \\ =5000 \times 30=150000 \mathrm{N} \end{gathered} $
This thrust gives upward force, $F=\frac{v d m}{d t}$
We also know that amount of gas ejected
$ \Rightarrow\left(\frac{d m}{d t}\right)=\frac{F}{v}=\frac{150000}{800}=187.5 $ $\mathrm{kg} / \mathrm{s}$
BETA
