Question

A rectangular block of mass 'm' and cross-sectional area 'A' floats on a liquid of density ρ. If it is given a small vertical displacement from equilibrium, it starts oscillating with frequency 'n' equal to ______.

(g = acceleration due to gravity)

Options

• `2pisqrt("m"/(Arhog))`

• `1/(2pi)sqrt((Arhog)/"m")`

• `2pisqrt((Arhog)/"m")`

• `1/(2pi)sqrt("m"/(Arhog))`

Answer 1

A rectangular block of mass 'm' and cross-sectional area 'A' floats on a liquid of density ρ. If it is given a small vertical displacement from equilibrium, it starts oscillating with frequency 'n' equal to `underline(1/(2pi)sqrt((Arhog)/"m"))`.

Explanation:

`T=2pisqrt(l/g)`     l = length of block dipped in liquid

Now, mg = Alρg

`l="m"/(Arho)`

`T=2pisqrt("m"/(Arhog))`

`thereforen=1/T=1/(2pi)sqrt((Arhog)/"m")`