Question

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.
A. 1.0 N
B. 3 N
C. 5 N
D. 6 N

Answer 1

Correct Answer - A

`implies` Liquid A is applying the hydrostatic force on cylinder from all the sides. So, net force is zero.
`implies` in equilibrium weight of cylinder `=` Net upthust on the cylinder
`impliess(h+h_(A)+h_(B))rho_("cylinder")=g=sg(h_(A)rho_(A)+h_(B)rho_(B))`
Where s is the base area of cylinder
`:. ` Net acceleration `=` force/mass of cylinder
`=(shrho_(B)g)/(s(h+h_(A)+h_(b))rho_("cylinder"))=g//6`