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Question

A cart of total mass 50 kg is at rest on a horizontal road having coefficient of friction 0.1. Gases are ejected from this cart backwards with velocity 20 m/s w.r.t the cart. The rate of ejection of gases is 2 kg/s. The cart will start moving after time :
[Take g=10 m/s2]


A
t=2 s
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B
t=3 s
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C
t=5 s
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D
t=10 s
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Solution

The correct option is C t=5 s
Given,
Mass of cart (m0)=50 kg
Relative velocity of gas ejected (vr)=20 m/s
Cart will start moving when the thrust force due to the gas overcomes the limiting force of friction.
i.e μmg=vr(dmdt)
Here, mass at time t,m=502t
0.1×(502t)×10=20×2
t=5 s

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