A mass m is suspended from a spring of length l and force constant K . The frequency of vibration of the mass is `f_(1)`. The spring is cut into two equal parts and the same mass is suspended from one of the parts. The new frequency of vibration of mass is `f_(2)` . Which of the following relations between the frequencies is correct

Options

A. `f_(1)=sqrt(2)f_(2)`
B. `f_(1)=f_(2)`
C. `f_(1)=2f_(2)`
D. `f_(2)=sqrt(2)f_(1)`

Answer

D

Explanation

Since, frequency `(f)prop sqrtk`
`(f_(1))/(f_(2))=sqrt((K_(1))/(K_(2)))=sqrt((K)/(2K))implies f_(2)=sqrt(2)f_(1)`.