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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-
$\frac{{Pm}}{{M + m}}$
$\frac{{Pm}}{{M - m}}$
$P$
$\frac{{PM}}{{M + m}}$
Solution
Consider the system as a whole
A block of mass $M$ and a rope tied to it of mass $m$ pulled by a force $P$ The only external force
The system will accelerate due to the action of the force, all accelerating with same acceleration
Acceleration of the system $=\frac{\text { Total external force }}{\text { Total mass }}$
$a=\frac{P}{m+M}$
Therefore acceleration of the block of mass $M$ will also be a
Net force on it $=m a s s \times$ acceleration
This force is force of the rope on the block
Hence $F=\frac{P M}{m+M}$
