The periodic time of a simple pendulum, oscillating in air is T. But if the bob of the simple pendulum is completely immersed in a nonviscous liquid, whose density is `(1)/(20)` th of the material of the bob, then its new period will be

Options

A. T
B. `(19)/(20)T`
C. `(20)/(19)T`
D. `sqrt((20)/(19))T`

Answer

D

Explanation

When the bob of the simple pendulum is immersed in a liquid, the effective weight of the bob
=mg-upthrust of the liquid (mg')
But `mg'=v xx d xxg -v xx (d)/(20)xx g= vdg (1-(1)/(20))`
`therefore` The effective acceleration g'
`=g(1-(1)/(20))=(19)/(20)g`
But `T=2pi sqrt((l)/(g))`
`(T_(2))/(T_(1))= sqrt((g)/(g'))= sqrt((g)/((19)/(20)g))=sqrt((20)/(19))`
`therefore T_(2)=sqrt((20)/(19))T_(1)`