A wooden cube (density of wood 'd') of side 'l' floats in a liquid of density `'rho'` with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period 'T'. Then, 'T' is equal to :

Options

A. `2pi sqrt((ld)/(rho g))`
B. `2pi sqrt((l rho)/(dg))`
C. `2pi sqrt((ld)/((rho-d)g))`
D. `2pi sqrt((ld)/((rho-d)g))`

Answer

A

Explanation

Restoring force,
`F=mg-F_(b).` br> `F="mg"-rhoA(l_(0)+x)g`
`dA l a=dAlg-rho A l_(0)g-rho g A x`
`a=-(rho g)/(d l)x`
`omega=sqrt((rho g)/(d l))`
`T=2pi sqrt((l d)/(rho g))`
So, correct choice is (a).