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Question

A cart of mass M is tied at one end of a massless rope of length 10 m. The other end of the rope is in the hands of a man of mass M. The entire system is on a smooth horizontal surface. Initially, the man is at x = 0 and the cart at x = 10 m. If the man pulls the cart using the rope, the man and the cart will meet at the point


A

x = 0

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B

x = 5 m

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C

x = 10 m

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D

They will never meet.

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Solution

The correct option is B

x = 5 m


Since there is no external force on the man-cart system in the horizontal direction, the centre of mass will not shift. Since their masses are equal, the centre of mass is located at the mid-point between them, i.e. at x = 5 m. Hence, they will meet at x = 5 m and the correct choice is (b).


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