Question

A plank of area of cross section A and
mass n is half immersed in liquid
I of density p and half in rigid 2
of densory ap , what is period of
collision Oscillarion of plank if it
is slightly de pressed downwards
1-2 Р​

Answer 1

Given :

Area of cross-section of plank = A

Mass of the plank = m

Density of the liquid 1 = ρ

Density of the liquid 2 = 2ρ

To Find :

The time period of the oscillation of the plank

Solution :

• The Buoyancy force acts on the block if it is given a downward displacement

• Buoyancy force = $-2xAg-(-xAg)$

                              = $-xAg$

• This buoyancy force acts as restoring force

         $ma = -Agx$

         $a = \frac{-Agx}{m}$

         $a = -\omega ^{2} x$

• As it is clear that the accelartion of a particle is proportional to its displacement the motion is SHM

• Time period of the particle = $T = \frac{2}{\omega}$

                                                        $T = \frac{2m}{Ag}$

The time period of oscillation of the plank is (2m/Ag) sec