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. `5//6`
B. `6//5`
C. 1
D. `4//5`

Answer

B

Explanation

`y = kt^(2)`
`:. (dy)/(dt) = 2kt`
`rArr (d^(2)y)/(dt^(2)) = 2k = 2 m//s^(2)`…(i)
`(because k = 1 m//s^(2), given)`
we know that
`T = 2 pi sqrt((l)/(g))`
`:. (T_(1)^(2))/(T_(2)^(2)) =(g_(2))/(g_(1)) rArr (T_(1)^(2))/(T_(2)^(2)) = (12)/(10) =(6)/(5)`
`[because g_(1) =10 m//s^(2), g_(2) =g+2=12 m//s^(2)]`.