A cylindrical piece of cork of density ρ of base area A and height h floats in a liquid of density ρ prime . The cork is slightly depressed and then released. The time period of oscillation of the cork is

Question

A cylindrical piece of cork of density ρ of base area A and height h floats in a liquid of density ρ prime . The cork is slightly depressed and then released. The time period of oscillation of the cork is (A) π √(g ρ prime/g ρ) (B) π √(h ρ/g ρ prime) (C) 2 π √(h ρ prime/g ρ) (D) 2 π √(h ρ/g ρ prime)

Tardigrade Admin · Accepted Answer

At equilibrium while floating,
Weight = Upthrust i.e

m g = (ρ^{'} A y_{0}) g

where

y_{0}

is the immersed length of the cork

\Rightarrow (ρ A h) g = (ρ^{'} A y_{0}) g

When the cork is further immersed by

y

and released, then

F = (m g) - ρ^{'} A (y + y_{0}) g = ρ^{'} A y_{0} g - ρ^{'} A y g - ρ^{'} A y_{0} g

F = - (ρ^{'} A g) y

\Rightarrow T = 2 π \frac{m}{k} = 2 π \frac{ρ A h}{ρ ^{'} A g}

= 2 π \frac{h ρ}{g ρ ^{'}}

Q. A cylindrical piece of cork of density $ρ$ of base area $A$ and height $h$ floats in a liquid of density $ρ^{'} .$ The cork is slightly depressed and then released. The time period of oscillation of the cork is

$π \frac{g ρ ^{'}}{g ρ}$

$π \frac{h ρ}{g ρ ^{'}}$

$2 π \frac{h ρ ^{'}}{g ρ}$

$2 π \frac{h ρ}{g ρ ^{'}}$

Q. A cylindrical piece of cork of density ρ of base area A and height h floats in a liquid of density ρ′. The cork is slightly depressed and then released. The time period of oscillation of the cork is

πgρgρ′​​

πgρ′hρ​​

2πgρhρ′​​

2πgρ′hρ​​

Q. A cylindrical piece of cork of density $ρ$ of base area $A$ and height $h$ floats in a liquid of density $ρ^{'} .$ The cork is slightly depressed and then released. The time period of oscillation of the cork is

$π \frac{g ρ ^{'}}{g ρ}$

$π \frac{h ρ}{g ρ ^{'}}$

$2 π \frac{h ρ ^{'}}{g ρ}$

$2 π \frac{h ρ}{g ρ ^{'}}$