A block is hanging at one end of the massless rope passing over a fixed smooth pulley. From other end of the rope a man of same mass climbs with an acceleration "x" relative to the acceleration of rope which is a. The value of "x" is :

Question

A block is hanging at one end of the massless rope passing over a fixed smooth pulley. From other end of the rope a man of same mass climbs with an acceleration "x" relative to the acceleration of rope which is a. The value of "x" is :

Answer 1

Magnitude of acceleration of string equals acceleration of block.
For man, T−Mg=Ma_man
​For block, T−Mg=Ma
∴a=a_man.
String accelerates downwards with a, and man acclerates upwards with a.
Hence relative acceleration x=2a