A simple pendulum with a metallic bob has a time period T. IF the bob is immersed in a non viscous liquid and its time period is measured as 4 T, then the ratio of densitites of metal bob to that of the liquid will be

Options

A. `15 : 16`
B. `16 : 15`
C. `1 : 16`
D. `16 : 1`

Answer

B

Explanation

`T_(2)=2pisqrt((l)/(g((rho_(m)-rho_(e))/(rho_(m)))))`
`T_(2)=(T)/(sqrt(((rho_(m)-rho_(e))/(rho_(m))))) because T=2pisqrt((l)/(g))`
`4T=(T)/(sqrt((rho_(m)-rho_(e))/rho_(m)))`
`16=(1)/(sqrt((rho_(m)-rho_(l))/(rho_(m))))`
`(rho_(m)-rho_(l))/(rho_(m))=(1)/(16)`
`1-(rho_(l))/(rho_(m))=(1)/(16)`
`1-(1)/(16)=(rho_(l))/(rho_(m))`
`(16-1)/(16)=(rho_(l))/(rho_(m))`
`(rho_(m))/(rho_(l))=(16)/(25)`.