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. `sqrt(2)f_(0)`
C. `2f_(0)`
D. `2sqrt(2)f_(0)`

Answer

B

Explanation

`f_(0) =1/(2pi) sqrt((mgl)/I)`
Where, l is 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((mgL/2)/((mL^(2)//12)))=1/(2pi) sqrt((6g)/L)`
When bottom half of the stick is cut of
`f'_(0)=1/(2pi) sqrt((m/2.g.L/4)/(m/2((L//2)^(2))/12))`
`=1/(2pi)xxsqrt((12g)/L) =sqrt(2)f_(0)`