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Question

PSLV decides to send a rocket to the moon for which it requires a velocity of 1232.6 m/s after 1 min. The rocket burns fuel at the rate of 10 kg/s. The burnt matter is ejected vertically downwards with a speed of 2000 m/s relative to the rocket. Calculate the initial mass of rocket. [Take g=10 m/s2]

A
400 kg
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B
1000 kg
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C
500 kg
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D
200 kg
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Solution

The correct option is B 1000 kg
Given,
Velocity of rocket after 1 min, v=1232.6 m/s
Fuel burn rate =dMdt=10 kg/s=μ
Speed of ejecting burnt matter Vr=2000 m/s
Initial mass =m0

Using the velocity equation: v=ugt+vrln(m0m)
Here,
m=m0μt=m010×60=m0600
Therefore,
1232.6=010×60+2000×ln(m0m0600)
0.9163=ln(m0m0600)
m0=1000 kg

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