A spring is connected to a mass m suspended from it and its time period for vertical oscillation is T. spring is now cut into two equal halved and the same mass is suspended fron one of the havles. The period of vertical oscillation is :

Options

A. `T'=sqrt(2)T`
B. `T'=(T)/(sqrt(2))`
C. `T'= sqrt(2T)`
D. `T'= sqrt((T)/(2))`

Answer

B

Explanation

`T=2pi sqrt((m)/(k))`
When the spring is cut into two equal halves, then the force constant of each part is 2k.
When the mass is suspended from one of the halves.
Time peirod `T'= 2pi sqrt((m)/(2k))`
`=(T)/(sqrt(2))`