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A 400 kg rocket is set for vertical firing. Exhaust speed of the gases is $490 m/s$ . The rate at which gas is to be ejected to give an upward acceleration of ‘g’ to the rocket

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$8 kg/s$

$16 kg/s$

$160 kg/s$

$1.6 kg/s$

answer is D.

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Detailed Solution

$m = 400 kg$

$V = 490 m/s$

When rocket is moving up we can have

$Mg - upthrust = 0$

$Mg = upthrust = \frac{dm}{dt} V$

$\frac{dm}{dt} = ?$

$g = 9.8 {m/s}^{2}$

$\frac{dm}{dt} = \frac{mg}{V} = \frac{400 \times 9.8}{490} = 8 kg/s$ $\frac{dm}{dt} = 8 kg/s$

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