Question

A block of mass M is tied to a fixed point C on a horizontal table through a string passing round a massless smooth pulley B. A force F is applied applied by the experimenter to the pulley. If the pulley is displaced by a distance x, then by what distance is the block displaced? Find the acceleration of the block and the pulley.

Answer 1

Initially length of string is, l1+l2=l (constant)
Let pulley and block are displaced by distance x1 and x2 respectively.
(l1+x1+x1)+(l2−x2)=l⇒2x1=x2
block will be displaced by 2x .
Differentiating twice we get acceleration of pulley (a1) and acceleration of​ block(a2) as,
2a1=a2
Now, for pulley,
F−2T=0⇒T=F2
For block,
a2=Tm=F2m
a1=F4m.