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Question

The figure shows a man of mass $$m$$ standing at the end $$A$$ of a trolley of mass $$M$$ placed at the rest on a smooth horizontal surface. The man starts moving towards the end $$B$$ with a velocity $$u_{rel}$$ with respect to the trolley. The length of the trolley is $$L$$.
Choose the correct statement:

A
The distance moved by the trolley is independent of the speed of the man
B
As the man starts moving the trolley must move backward
C
All of the above.
D
The distance moved by the trolley can never exceed $$L$$
Solution
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Correct option is D. All of the above.
Since no external force acts on system center of mass remains stationary.

So, if man moves forward then trolley moves backward.

The center of mass remains same so the distance moved by trolley depends on distance moved by man.

Since the center of mass lying in between of the 'M' and 'm' and if the man be at any position exceeding 'L' then center of mass will move which contradict the fact that center of mass remains fixed.
Hence trolley can never exceed 'L'.

So all the above options are correct

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