A simple pendulum has time period (T_1). The point of suspension is now moved upward according to the relation `y = K t^2, (K = 1 m//s^2)` where (y) is the vertical displacement. The time period now becomes (T_2). The ratio of `(T_1^2)/(T_2^2)` is `(g = 10 m//s^2)`.

Options

A. `2//3`
B. `5//6`
C. `6//5`
D. `3//2`

Answer

C

Explanation

`T_1=2pisqrt(L/g)`
`y=kt^2=t^2`
`(dy)/(dt)=2t`
`(d^2y)/(dt^2)=2=a_0`

`T_2=2pisqrt((L)/(g+a_0))`
`T_1/T_2=sqrt((g+a_0)/(g))=sqrt((10+2)/(10))=sqrt(6/5)`
`T_1^2/T_2^2=6/5`