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

A)  \[\frac{Pm}{M+m}\]                     

B)  \[\frac{Pm}{M-m}\]

C)  \[P\]                    

D)         \[\frac{PM}{M+m}\]

Correct Answer: D

Solution :

Let acceleration of system (rope + block) is an along the direction of applied force. Then                 \[a=\frac{P}{M+m}\] Draw the FBD of block and rope as shown in figure. where, \[T\] is the required parameter For block      \[T=Ma\] \[\Rightarrow \]               \[T=\frac{MP}{M+m}\]