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Question

Initial fuel in a rocket is 1000kg. If it was given an acceleration of 20ms2 the velocity of fuel with respect to the rocket is 500ms. Find the rate of consumption of fuel.


A

30kgs

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B

60kgs

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C

900kgs

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D

80kgs

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Solution

The correct option is B

60kgs


Solution:

Step 1: Given information

Initial fuel=1000kg.

Acceleration=20ms2

Fuel's velocity=500ms

Step 2: Calculate the rate of consumption of fuel

Know that, given a system with variable mass,

TotalForce(Byrocket)-GravitationalForce=ActingForce,

fTmg=ma…..(i)

Where,

fT=Total force

m=Mass of fuel

g=Acceleration due to gravity

a=Acceleration produced by rocket

Therefore, from equation (i),

mvrtmg=ma…..(ii)

Where, (fT=m×a)

Step 3: Solving by putting the given values in the equation (ii)

Therefore, from equation (ii),

dmdtvr=mg+ma

dmdt500=1000(10+20)

dmdt=60kg/s

Hence, the correct option is (B).


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