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Question

# Scientists of ISRO want to achieve a velocity of rocket 100 m/s after time t=5 sec. Velocity of ejected burnt fuel is 20 m/s w.r.t the rocket. What should be the rate of consumption of fuel (approximately) so that the rocket will achieve the desired velocity? Initial mass of rocket is 2000 kg. [Take g=10 m/s2]

A
300 kg/s
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B
400 kg/s
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C
100 kg/s
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D
200 kg/s
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Solution

## The correct option is B 400 kg/sGiven, Initial mass of rocket m0=2000 kg. Velocity of rocket after 5 sec v=100 m/s Initial velocity u=0 m/s Velocity of ejected burnt fuel vr=20 m/s As we know, v=u−gt+vrln(mom) Here m=m0−μt =2000−μ×5 ...(1) Then, 100=0−10×5+20×ln(20002000−5μ) ⇒7.5=ln(20002000−5μ) ⇒1808.04=20002000−5μ ⇒μ=399.78 kg/s≈400 kg/s

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