A cubical body (side `0.1m` and mass `0.002kg)` floats in water. It is pressed and then released so that it executes SHM. Find the time period. `(g=10m//s^(2))`

Explanation

When a floating cubical body is displaced down through a small distance x the excess buoyant force that is known as the restoring force is given as
`F = -v rho g`
Where v = volume of the excess liquid displaced = Ax
`rArr F = -A rho g x , A=` area of cross section of the cube.
`rArr -m omega_(osc)^(2) x = - A rho g x`
`rArr omega_(osc) = sqrt((A rho g)/(m))`
`m = 0.02 kg. rho = 10^(3) kg//m^(3), A = (0.1)^(2) m^(2)`
`T = 2pi sqrt((m)/(A rho g)) = 0.0885 sec`