Two blocks of mass M and m are kept on a trol | vedclass

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(D) The system consists of a trolley of mass $M_0$ and two blocks of mass $M$ and $m$ connected by a string over a pulley. All surfaces are smooth.If

Vedclass · Accepted Answer

Both $(a)$ and $(b)$ are correct.

Vedclass · Answer

(D) The system consists of a trolley of mass $M_0$ and two blocks of mass $M$ and $m$ connected by a string over a pulley. All surfaces are smooth.If $F=0$,the system is not accelerating,but the block $m$ will experience a gravitational force pulling it downwards,causing it to move. Thus,the blocks cannot remain stationary.If the trolley accelerates with acceleration $a = F / (M + m + M_0)$,a pseudo force acts on the blocks in the frame of the trolley. For the blocks to be stationary relative to the trolley,the forces acting on them must balance. Specifically,for block $m$,the pseudo force $ma$ must balance the tension $T$,and for block $M$,the tension $T$ must balance the pseudo force $Ma$. This requires $ma = T$ and $T = Ma$,which implies $m=M$. If $M=m$,there exists a unique value of $F$ that makes the system stationary relative to the trolley. Since the question implies a general case where such a condition can be met,both statements $(a)$ and $(b)$ are correct.

Two blocks of mass $M$ and $m$ are kept on a trolley of mass $M_0$ as shown in the figure. All surfaces are smooth. Select the correct statement.

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