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(C) Let the velocity of mass $M$ be $v$ in the upward direction.Consider the segment of the string passing over pulley $A$. The velocity of the string

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$\frac{U}{\cos 	heta}$

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(C) Let the velocity of mass $M$ be $v$ in the upward direction.Consider the segment of the string passing over pulley $A$. The velocity of the string along the segment connected to $M$ is $v$. The component of this velocity along the direction of the string towards pulley $A$ must be equal to the speed $U$ at which the end $P$ is pulled.Therefore,$v \cos 	heta = U$.Solving for $v$,we get $v = \frac{U}{\cos 	heta}$.Thus,the mass $M$ moves upwards with a speed of $\frac{U}{\cos 	heta}$.

In the arrangement shown in the figure,the ends $P$ and $Q$ of an unstretchable string move downwards with a uniform speed $U$. Pulleys $A$ and $B$ are fixed. The mass $M$ moves upwards with a speed:

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