The bob of a simple pendulum executm 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. `t = t_(0)`
B. `t = t_(0)//2`
C. `t =2 t_(0)`
D. `t = 4t_(0)`

Answer

C

Explanation

`:' t_(0)= 2pi sqrt((1)/(g))`
Effectiveweight of bob inside water
`W' = mg - thrust = Vpg - Vp^(2)g`
`rArr Vrhog_(eff) - V(rho- rho')g` where `rho=` Density of water
`rArr g_(eff) = (1 -(g^(2))/(p))g` and `rho' =` Density of water
`:. T = 2pi sqrt((1)/(g_(eff))) = 2pi sqrt((1)/((1-p'//p)g))`
`:.(t)/(t_(0)) = sqrt((1)/(1-p//p)) = sqrt((1)/(1 - (3)/(4))`
`(:' p' = 10^(2) kg//m^(2)` and `rho = (4)/(3) xx 10^(3) kg//m^(3)`)
`rArr t = 2s_(0)`