The bob of a simple pendulum execute simple harmonic motion in water with a period `t`, while the period of oscillation of the bob is `t_(0)` in air. Negleting frictional force of water and given that the density of the bob is `(4//3)xx1000 kg//m^(3)`.
What relationship between `t `and `t_(0)` is true.

Options

A. (a)`t =t_(0)`
B. (b)`t = t_(0)//2`
C. (c)`t = 2t_(0)`
D. (d)`t = 4t_(0)`

Explanation

The time period of a simple pendulum of density `rho` when held in a surrounding of density `sigma` is
`t_("medium") = t_(air)sqrt((rho)/(rho - sigma))`
`rArr t_("water") = t_(0)sqrt((4/3xx10^(-3))/((4/3-1)xx10^(-3))) = t_(0)sqrt((4)/(3) xx (3)/(1)) = 2t_(0)`