Question

# Mr. Verma (50 kg) and Mr. Mathur (60 kg) are sitting at the two extremes of a 4 m long boat (40 kg) standing still in water. To discuss a mechanics problem, they come to the middle of the boat. Neglecting friction with water, how far does the boat move in the water during the process?

A
2 m
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B
1/15 m
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C
2/15 m
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D
3/15 m
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Solution

## The correct option is C 2/15 m Let displacement of the boat is Xb=x towards right The displacement of Mr. Verma: Xv=(x+2)m The displacement of Mr. Mathur: Xm=(x−2)m As no external forces are acting on the system, the displacement of the centre of mass of the system should be zero. ΔxCM=Mbxb+Mvxv+Mmxm(Mb+Mv+Mm) ∴ 0=40x+50(x+2)+60(x−2)150⇒x=2/15 m

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