Question

Q. A \(5000 \mathrm{~kg}\) rocket is set for vertical firing. The exhaust speed is \(800 \mathrm{~m} / \mathrm{s}\). To give an initial upward acceleration of \(20 \mathrm{~m} / \mathrm{s}^{2}\), the amount of gas ejected per second to supply the needed thrust will be \(\left(\right.\) Take \(\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}\right)\)
A \(127.5 \mathrm{~kg} / \mathrm{s}\)
B) \(137.5 \mathrm{~kg} / \mathrm{s}\)
C \(155.5 \mathrm{~kg} / \mathrm{s}\)
(D) \(187.5 \mathrm{~kg} / \mathrm{s}\)

Answer 1

Solution:
Given : Mass of rocket \((m)=5000 \mathrm{Kg}\)
Exhaust speed \((v)=800 \mathrm{~m} / \mathrm{s}\)
Acceleration of rocket \((\mathrm{a})=20 \mathrm{~m} / \mathrm{s}^{2}\)
Gravitational acceleration \((g)=10 \mathrm{~m} / \mathrm{s}^{2}\)
We know that upward force
\(F=m(g+a)=5000(10+20)\)
\(=5000 \times 30=150000 \mathrm{~N}\).
We also know that amount of gas ejected
\(\left(\frac{d m}{d t}\right)=\frac{F}{V}=\frac{150000}{800}=187.5 \mathrm{~kg} / \mathrm{s}\)

Answer 2

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