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  Solved  Paper-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 :

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)]