A block of mass `m` is attached to a pulley disc of equal mass `m` and radius `r` by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of `5 m//s`. Its velocity when the string becomes taut will be

Options

A. 3 m/s
B. `2.5` m/s
C. `5//3` m/s
D. `10//3` m/s

Answer

D

Explanation

Let J: impulse generated in the string `rArr J=1/2 mr^(2)omega`….. For pulley
For block, `-J = mv_(2) -mv`…. And `v_(2) =romega`
where `v_(2)` is velocity of the block just after the string becomes taut.
`rArr 0=(mv_(2))/2 + mv_(2) -mv rArr v_(2) =(2v)/3 =10//3 m//s`