As shown in fig., a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass 2m. when released from rest the bob starts falling vertically. The time taken by the bob to descend through a height h, from the initial position, is

Options

A. `2sqrt(h/g)`
B. `sqrt((2h)/g)`
C. `sqrt((4h)/(3g))`
D. `sqrt((2h)/(3g))`

Answer

A

Explanation

`T.r=(2mr^(2))/(2)alpha`
`implies T=mralpha` . . (i)
`mg-T=ma=mralpha`
`implies mg=2mralpha implies ralpha=(g)/(2)=a`.
`therefore h=0+(1)/(2)((g)/(2))t^(2) implies t=sqrt((4h)/(g))=2sqrt((h)/(g))`.