Question

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 :

• A. $\frac{PM}{M+m}$
• B. $\frac{PM}{M-m}$
• C. $\frac{Pm}{M+m}$
  
• D. $\frac{Pm}{M-m}$
  

Answer 1

The correct option is A $\frac{PM}{M+m}$

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 = $\frac{Totalexternalforce}{Totalmass}$

$a$ = $\frac{P}{m+M}$

Therefore acceleration of the block of mass $M$ will also be $a$

Net force on it = $mass$ x $acceleration$

This force is force of the rope on the block

Hence $F$ = $\frac{PM}{m+M}$