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Question

A boat of length 10 m and mass 450 kg is floating without motion in still water. A man of mass 50 kg standing at one end of it walks to the other end of it and stops.
 The magnitude of the displacement of the boat in meters relative to ground is


A
Zero
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B
1 m
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C
2 m
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D
5 m
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Solution

The correct option is B 1 m
Centre of mass will not be displaced, thus 
There is no horizontal external force,
$$\Delta X_{cm}=0$$
$$ { m }_{ 1 }{ x }_{ 1 }+{ m }_{ 2 }x_{ 2 } =0$$
$$ Now,\ let\ { x }_{ 1 }= x,\quad then\quad { x }_{ 2 } =-(10 -x)$$
(because distance covered by man relative to boat $$=$$ 10 m or
$$x_2 - (-{ x }_{ 1 })=10,\quad in\quad opposite\quad direction)\\$$
$$Thus,\ 450x -50(10-x)=0\quad or\quad x =1\ m$$

Physics

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