A cylinderical block of wood of mass m and area cross-section A is floating in water (density = `rho`) when its axis vertical. When dressed a little and the released the block starts oscillating. The period oscillations is

Options

A. `2pi sqrt(m/( rho Ag))`
B. `2pi sqrt((mg)/(rho a))`
C. `2pi sqrt((rho Ag)/m)`
D. `2pi sqrt((rho A)/(mg))`

Answer

A

Explanation

When depressed by `x` from its mean positioin extra upthrust
`=` restoring force `(F)`
or `F=-(A rho x g)`
Since `F prop -x`
Oscilations are simple harmonic.
`:.` Acceleration of block
`a=F/m=-((A rhog)/m)`
Now `T=2pi sqrt(|x/a|)`
`=2pi sqrt(m/(rho A g))`