The matallic bob of a simple pendulum has the relative density `rho`. The time period of this pendulum is `T` it the metallic bob is immersed in water the new time period is given by

Options

A. `T ((rho - 1)/(rho))`
B. `T ((rho)/(rho - 1))`
C. `T sqrt((rho - 1)/(rho))`
D. `T sqrt((rho)/(rho - 1))`

Answer

C

Explanation

`mg^(1) = mg - V rho g rArr g^(1) = g (1 - (rho)/(rho s))`
`(T^(1))/(T) = sqrt((rho s)/(rho s - rho))=sqrt((rho)/(rho-1))`