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Question

# A rocket of mass 3000 kg is launched with an exhaust speed of the gas v=50 m/s. What will be the acceleration of the rocket after 3 sec, if the rate of consumption of fuel is 600 kg/s? (Take g=10 m/s2)

A
0 m/s2
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B
35 m/s2
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C
6 m/s2
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D
15 m/s2
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Solution

## The correct option is D 15 m/s2Given, Mass of rocket; M=3000 kg Exhaust speed of gas, v=50 m/s Loss of mass of rocket in 1 sec is 600 kg so, ∴Loss of mass of rocket in 3 sec is 3×600=1800 kg So mass of rocket after 3 sec; M′=3000−1800=1200 kg ∴M′=1200 kg, v=50 m/s dmdt=600 kg/s,g=10 m/s2 As we know, v.dmdt−M′g=M′a 50×(600)−(1200)×10=(1200)×a a=15 m/s2

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