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(D) Consider the system consisting of the block of mass $M$ and the rope of mass $m$ as a single unit.The total mass of the system is $(M + m)$.$A$ ho

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$\frac{PM}{M + m}$

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(D) Consider the system consisting of the block of mass $M$ and the rope of mass $m$ as a single unit.The total mass of the system is $(M + m)$.$A$ horizontal force $P$ is applied to the free end of the rope,which acts as the net external force on the system.According to Newton's second law,the acceleration $a$ of the system is given by:$a = \frac{	ext{Total Force}}{	ext{Total Mass}} = \frac{P}{M + m}$Since the block and the rope move together,the block of mass $M$ also moves with the same acceleration $a$.The force exerted by the rope on the block is the net force required to accelerate the block of mass $M$:$F = M 	imes a$Substituting the value of $a$:$F = M 	imes \left( \frac{P}{M + m} ight) = \frac{PM}{M + m}$

$A$ block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is applied at the free end of the rope,the force exerted by the rope on the block is-

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