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

Options

A. `("Pm")/(M+m)`
B. `("Pm")/(M-m)`
C. P
D. `("PM")/(M+m)`

Answer

D

Explanation

Let acceleration of system (rope + block) is a which is acting along the direction of applied force. Then,

`a=(P)/(M+m)`
Draw the FBD of block and rope as shown in figure.

where, T is the required parameter.
For block, T = Ma
`implies" "T=(MP)/(M+m)`