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Question

A rocket of mass 4000 kg is set for vertical firing. How much gas must be ejected per second so that the rocket may have initial upwards acceleration of magnitude 19.6 m/s2? [Exhaust speed of fuel =980m/s]

A
240 kg/s
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B
80 kg/s
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C
120 kg/s
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D
None
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Solution

The correct option is C 120 kg/s
For upward motion of rocket, thrust force must be greater in magnitude than its weight and net force will be equal to their difference, i.e.,
Upward thrustWeight=Fnet
vedmdtmg=ma
dmdt=ma+mgve

Here, negative sign is implying that mass of gas is decreasing with the passage of time and ve=980 m/s is the exhaust speed of fuel.
Hence dmdt=m(a+g)ve
dmdt=4000(19.6+9.8)980
dmdt=120kg/s

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