A 6000 kg rocket is set for vertical firing. If the exhaust speed is 1000 m/sec. How much gas must be ejected each second to supply the thrust needed to overcome the weight of rocket.
(consider $g = 9.8 m / s^{2}$ acceleration due to gravity )

6 k g / s e c

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60 k g / s e c

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600 k g / s e c

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6000 k g / s e c

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Solution

The correct option is A $60 k g / s e c$
Given,

Mass, $m = 6000 k g$

We have the formula for thrust,

$F = u \times \frac{d m}{d t}$

Now,

$T h r u s t = W e i g h t$

Then,

$1000 \times \frac{d m}{d t} = m g$

$1000 \times \frac{d m}{d t} = 6000 \times 10$

$\frac{d m}{d t} = 60 k g / s$

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