A metre stick swinging in vertical plane about a fixed horizontal axis passing through its one end undergoes small oscillation of frequency `f_0`. If the bottom half of the stick were but off, then its new frequency of small oscillation woul become.

Options

A. `f_0`
B. `sqrt2f_0`
C. `2f_0`
D. `2sqrt2f_0`

Answer

B

Explanation

`f_0=(1)/(2pi)sqrt((mgl)/(I))`
where `l` is the distance between point of suspension and centre of mass of the body. Thus, for the stick of length L and mass m,
`f_0=(1)/(2pi)sqrt((mg(L)/(4))/((m)/(2)(((L)/(2))^2)/(12)))=(1)/(2pi)sqrt((12g)/(L))=sqrt2f_0`