A cylinderical block of density d stays fully immersed in a beaker filled with two immiscible liquids of different densities `d_1` and `d_2` The block is in equilibrium with half of it in liquid 1 and the other half in liquid 2 as shown in the Fig. If the block is given a displacement downwards released, then neglecting friction study the following statements.

Options

A. it executes simple harmonic motion
B. it motion is oscillatory bu not `SHM`
C. frequency of oscillation depends on size of the cylinder
D. displacement of centre of cylinder is symmetric about its equilibrium position

Explanation

When the block is displaced slightly downwards.
Restarting force, `F_(R )=Axgd_(2)-Axgd_(1)`
`F_(R )=Agx(d_(2)-d_(1))(SHM)`
`rArr omega=sqrt((G(d_(2)-d_(1)))/(Ld_(E)))`