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(D) Since the system (man + trolley) is on a smooth horizontal surface,there is no external horizontal force acting on it. Therefore,the center of mas

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All the above.

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(D) Since the system (man + trolley) is on a smooth horizontal surface,there is no external horizontal force acting on it. Therefore,the center of mass of the system remains at rest.Let $x_m$ and $x_t$ be the displacements of the man and the trolley with respect to the ground,respectively. Since the center of mass is stationary,$m x_m + M x_t = 0$.The man moves a distance $L$ relative to the trolley,so $x_m - x_t = L$,or $x_m = L + x_t$.Substituting this into the center of mass equation: $m(L + x_t) + M x_t = 0 \implies x_t(m + M) = -mL \implies x_t = -\frac{mL}{m+M}$.The negative sign indicates the trolley moves backward (opposite to the man's motion),so option $A$ is correct.The displacement of the trolley $x_t = \frac{mL}{m+M}$ depends only on the masses and the length $L$,not on the speed of the man,so option $B$ is correct.Since $x_t = \frac{m}{m+M} L$,and $\frac{m}{m+M} Therefore,all the statements are correct.

The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at 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.

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