Laws of Motion - Result Question 11
11. A $5000 kg$ rocket is set for vertical firing. The exhaust speed is $800 ms^{-1}$. To give an initial upward acceleration of $20 ms^{-2}$, the amount of gas ejected per second to supply the needed thrust will be $(g=10 ms^{-2})$
(a) $127.5 kg s^{-1}$
(b) $187.5 kg s^{-1}$
(c) $185.5 kg s^{-1}$
(d) $137.5 kg s^{-1}$
[1998]
Show Answer
Answer:
Correct Answer: 11. (b)
Solution:
- (b) Given : Mass of rocket (m) $=5000 kg$
Exhaust speed $(v)=800 m / s$
Acceleration of rocket $(a)=20 m / s^{2}$
Gravitational acceleration $(g)=10 m / s^{2}$
Thrust, $\Rightarrow \frac{v d m}{d t}$
We know that upward force,
$F=m(g+a)=5000(10+20)$
$=5000 \times 30=150000 N$
This thrust gives upward force, $F=\frac{v d m}{d t}$
We also know that amount of gas ejected
$\Rightarrow(\frac{d m}{d t})=\frac{F}{v}=\frac{150000}{800}=187.5 kg / s$
