A plank is floating in a non-viscous liquid as shown, Choose the correct option

Options

A. Equilibrium of plank is stable in vertical direction
B. For small oscillations of plank in vertical direction motion is simple harmonic
C. Even if oscillations are large, motion is simple harmonic till it is not fully immersed
D. On vertical displacement motion is periodic but not simple harmonic

Answer

A, B, C

Explanation

Restroing force `=-(rho Ag)x` or `F prop -x`
This is just like a spring - block system of force constant
`K=rho Ag`.