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Question

# A rocket of initial mass m=2000 kg is burning fuel at the rate of 20 kg/s and ejecting burnt matter with a constant speed of 1000 m/s w.r.t the rocket. Find the acceleration of the rocket at t=10 sec. [Take g=10 m/s2]

A
0
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B
0.55 m/s2
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C
1.11 m/s2
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D
2.3 m/s2
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Solution

## The correct option is C 1.11 m/s2 Given, initial mass of rocket = 2000 kg Rate of burning fuel μ=dMdt=20 kg/s and relative velocity of ejection of fuel Vr=−1000 m/s (downwards -ve) We know, for a variable mass system with constant rate of ejection: Fext−Vrdmdt=ma Here (−dmdt)and Vr will be constant through out the journey. ⇒−mg−(−1000×20)=ma Mass at t=10 sec m=2000−20×10=1800 kg ⇒1000×(20)−1800×10=1800×a ⇒a=1.11 m/s2

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