A $5000 k g$ rocket is set for vertical firing. The exhaust speed is $800 m / s$ . To give an initial upward acceleration of $20 m / s^{2}$ , the amount of gas ejected per second to supply the needed thrust will be (take $g = 10 m / s^{2})$

127.5 k g / s

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137.6 k g / s

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155.5 k g / s

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187.5 k g / s

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Solution

The correct option is D $187.5 k g / s$

$F_{n e t}$ = Upthrust - Weight of the rocket

When gas is ejected, the total mass of the rocket, $m$ decreases. Let the amount of gas ejected per second be $\frac{d m}{d t}$ .
Then Upthrust force $= \frac{d}{d t} (m v) = \frac{d m}{d t} v$ where $v$ is the exhaust speed.

Therefore, $F_{n e t} = \frac{d m}{d t} v - m g = m a$
$\Rightarrow \frac{d m}{d t} \times 800 - 5000 \times 10 = 5000 \times 20$
$\Rightarrow \frac{d m}{d t} = 187.5 k g / s$

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A 5000 kg rocket is set for vertical firing. The exhaust speed is 800 m/s. To give an initial upward acceleration of 20 m/s2, the amount of gas ejected per second to supply the needed thrust will be (take g=10 m/s2)

A $5000 k g$ rocket is set for vertical firing. The exhaust speed is $800 m / s$ . To give an initial upward acceleration of $20 m / s^{2}$ , the amount of gas ejected per second to supply the needed thrust will be (take $g = 10 m / s^{2})$