An object of mass M is tied to a string of l and revolve in a horizontal circle .If length is reduced by `l//2`, then period is

Options

A. `T//sqrt2`
B. `2sqrt2 T`
C. `T//4`
D. `2 T`

Answer

C

Explanation

`omega =(2 pi)/(T)=(v)/(l)`
Accounding to the law of conservation of angular momentum ,
`m_(1)v_(1)r_(1)=m_(2)v_(2)r_(2)`
`therefore r_(1)^(2) omega _(1)=r_(2)^(2)omega _(2)implies (r_(1)^(2))/(T_(1))=r_(2)^(2)/(T_(2))`
`therefore T_(2)=((r_(2)^(2))/r_(1)^(2))T_(1)((l^(2)//4)/(l^(2)))T=(T)/(4)`.