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A boy having ...

Question

A boy having a mass of 40 kg stands at one end A of a boat of length 2 m at rest. The boy walks to the other end B of the boat and stops. What is the distance moved by the boat? Friction exists between the feet of the boy and the surface of the boat. But the friction between the boat and the water surface may be neglected. Mass of the boat is 15 kg.

0.49 m

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2.46 m

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1.46 m

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3.2 m

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Solution

The correct option is D 1.46 m
Centre of mass will not be displaced, thus
$m_{1} x_{1} + m_{2} x_{2} = 0 N o w, l e t x_{1} = x, t h e n x_{2} = - (2 - x)$
(because distance covered by man relative to boat $= 2 m$ or $x_{2} - (- x_{1}) = 2$ , in opposite direction)
Thus, $15 x - 40 (2 - x) = 0 o r x = 1.46 m$

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The correct option is D 1.46 mCentre of mass will not be displaced, thus m1x1+m2x2=0Now,letx1=x,thenx2=−(2−x)(because distance covered by man relative to boat =2m or x2−(−x1)=2, in opposite direction)Thus, 15x−40(2−x)=0orx=1.46m