A uniform solid cylinder of density `0.8g//cm^3` floats in equilibrium in a combination of two non-mixing liquids A and B with its axis vertical.
The densities of the liquids A and B are `0.7g//cm^3` and `1.2g//cm^3`, respectively. The height of liquid A is `h_A=1.2cm.` The length of the part of the cylinder immersed in liquid B is `h_B=0.8cm`.

(a) Find the total force exerted by liquid A on the cylinder.
(b) Find h, the length of the part of the cylinder in air.
(c) The cylinder is depressed in such a way that its top surface is just below the upper surface of liquid A and is then released. Find the acceleration of the cylinder immediately after it is released.

Answer

A, B, C

Explanation

(a) As the pressure exerted by liquid A on the cylinder is radial and symmetric, the force due to this pressure cancels out and the net value is zero.
(b) For equilibrium, Buoyant force =weight of the body
`impliesh_Arho_A Ag+h_Brho_BAg =(h_A+h+h_B)Arho_Cg`
(where `rho_C=` density of cylinder)
`h=((h_Arho_A+h_Brho_B)/(rho_C))-(h_A+h_B)=0.25cm`
(c) `a=(F_(Buoyant-Mg)/(M))`
`=[(h_Arho_A+rho_B(h+h_B)-(h+h_A+h_B)rho_C)/(rho_C(h+h_A+h_C))]g`
`=g/6` upwards