question_answer

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 [AIEEE 2003]

A) \[\frac{P\,m}{M+m}\]

B) \[\frac{P\,m}{M-m}\]

C)             P

D) \[\frac{P\,M}{M+m}\]

Correct Answer: D

Solution :

[d] Let acceleration of system (rope + block) is a along the direction of applied force. Then,

\[a=\frac{P}{M+m}\]                .. (i)

Frictionless surface

Draw the FBD of block and rope as shown in figure below.

where, T is the required parameter (i.e., force)

For block       T = Ma

\[\Rightarrow \]   \[T=\frac{MP}{M+m}\] [from Eq. (i)]