A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $P$ is

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 will be:

Accepted Answer

1. **Analyze the System:** 
   Consider the block and the rope as a single system. 
   - Total mass = $M + m$. 
   - Net external force = $P$ (applied at the end of the rope).

2. **Calculate Acceleration ($a$):** 
   Since the surface is frictionless, apply Newton's Second Law ($F = ma$) to the whole system:
   $$ P = (M + m)a $$
   $$ a = \frac{P}{M + m} $$

3. **Calculate Force on the Block:** 
   The force exerted by the rope on the block ($F_{block}$) is the tension at the junction between the rope and the block. This force is responsible for accelerating the block of mass $M$.
   $$ F_{block} = M 	imes a $$
   Substitute the value of $a$:
   $$ F_{block} = M \left( \frac{P}{M + m} ight) $$
   $$ F_{block} = \frac{PM}{M + m} $$
   (Reference: NCERT Class 11, Physics Part I, Chapter 5: Laws of Motion, Section 5.10 'Problems in Mechanics' - treating connected bodies).

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