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  4. A cart of mass M is tied to 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. The man is at x=0 and the cart at x=10 m . If the man pulls the cart by a rope, the man and the cart will meet at the point

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Q. A cart of mass $M$ is tied to 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. The man is at $x=0$ and the cart at $x=10 \, m$ . If the man pulls the cart by a rope, the man and the cart will meet at the point

NTA AbhyasNTA Abhyas 2022

Solution:

They meet at the centre of mass
$x_{C O M}=\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$
$=\frac{M \times 0 + M \times 10}{2 M}=5m$