A cube made of wood having specific gravity `0.4` and side length `a` is floated in a large tanck full of water.

If the cube is depressed slighly, it executes `SHM` from it's position. What is it's time period?

Options

A. `2pi sqrt((a)/(g))`
B. `2pi sqrt((5a)/(2g))`
C. `2pi sqrt((2a)/(5g))`
D. `(4pi)/(5)sqrt((a)/(g))`

Answer

C

Explanation

`mg = F_(b), a^(2) xx 0.4 rho g = a^(2) h rho g`
`h = (2)/(5)a, m = a ^(3) xx 0.4, F_(net) =a^(2) x rho g`
`T = 2pi sqrt((a^(3) xx 0.4 rho)/(a^(2) rho g)) , T = 2pi sqrt((2a)/(5g))`