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Question

A tank cart is filled with water as shown in the figure. The initial mass of the cart with water is m0=100 kg. At time t=0, a hole is made in the left wall of the cart and water starts spilling out from the cart, with a constant velocity of vr=10 m/s with respect to the cart. The rate of ejection of water is r=2 kg/s. Find the acceleration of the cart after time t=5 s.


A
0.11 m/s2
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B
0 m/s2
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C
0.22 m/s2
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D
0.4 m/s2
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Solution

The correct option is C 0.22 m/s2
Force of thrust on the cart
Ft=vrdmdt=10×2=20 N
(-ve sign indicates force is rightward)
Since there is no external force in horizontal direction,
Ft=ma

Acceleration of the cart a=Ftm
=Ftm0μt=vr(dmdt)m0μt

At t=5 s,
a=10×21002×5=0.22 m/s2
a=0.22 m/s2

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