Laws of Motion - Result Question 11

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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 $(g=10 ms^{-2})$

======= ####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 $(g=10 ms^{-2})$

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/laws-of-motion/laws-of-motion—result-question-11.md (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]

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Answer:

Correct Answer: 11. (b)

Solution:

  1. (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

$\Rightarrow(\frac{d m}{d t})=\frac{F}{v}=\frac{150000}{800}=187.5 kg / s$