Question

A plank of area of cross section A is half immersed in liquid 1 of density and half in liquid 2 of density 2. What is the period of oscillation of the plank, if it is slightly depressed downwards

Answer 1

Answer:

ANSWER

The net buoyancy force acting on the block if it is given a downward displacement x is = −2xAg−(−xAg)=−Agx

Since buoyant force acts as restoring force, we can write ma=−Agx or a=−(Ag/m)x=−w

2

x

Thus, acceleration is proportional to displacement and the motion is SHM.

The time period of oscillations T=2=2/w=2(m/Ag)