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Question

A rocket is in gravity free space. A scientist wants the acceleration of the rocket to be 2 m/s2. Initial mass of the rocket is 1000 kg and the speed of ejection of burnt fuel w.r.t the rocket is 500 m/s. Find the rate of consumption of fuel (in kg/s), so that the rocket will have an acceleration of 2 m/s2.

A
2 kg/s
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B
4 kg/s
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C
3 kg/s
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D
1 kg/s
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Solution

The correct option is B 4 kg/s
Given, initial mass of the rocket m=1000 kg
Acceleration of the rocket a=2 m/s2
Relative speed of ejection of burnt fuel vr=500 m/s


From equation of variable mass system,
Ft+Fext=ma
It is gravity free space, hence Fext=mg=0
& Ft=vrdmdt

i.e vr(dmdt)=ma
500×(dmdt)=1000×2
(relative velocity of ejection downward)
dmdt=4 kg/s
(-ve sign signifies mass is decreasing)

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