A mass m is suspended to a spring of length L and force constant k. The frequency of vibration is v. The spring is cut into two equal parts and each half is loaded with same mass m. The new frequency v' is given by :

Options

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

Answer

A

Explanation

Here `f_(1)=(1)/(2pi)sqrt((k_(1))/(m))`
and `" "k_(1)=(mg)/(DeltaL)`.
Now `" "k_(2)=(mg)/(DeltaL//2)=2k_(1)`
`f_(2)=(1)/(2pi)sqrt((2k_(1))/(m))`
and `f_(2)=sqrt(2)f_(1)`.
Correct choice is (a).