A solid sphere of radius `R` is floating in a liquid of density `sigma` with half of its volume submerged. If the sphere is slightly pushed and released , it starts axecuting simple harmonic motion. Find the frequency of these oscillations.

Options

A. `(1)/(2pi)sqrt((3g)/(2R))`
B. `(1)/(pi)sqrt((3g)/(2R))`
C. `(1)/(2pi)sqrt((3g)/(R))`
D. `(1)/(4pi)sqrt((3g)/(R))`

Answer

A

Explanation

For equilibrium density of sphere = p//2
If it is slightly displaced by x restoring force `F=(piR^(2)x)pg`
`T=2pisqrt((m)/(piR^(2)pg))=2pisqrt(((4)/(3)piR^(3)p//2)/(piR^(2)pg))=2pisqrt((2R)/(3g))` implies `f=(1)/(2pi)sqrt((3g)/(2R))`