The angular frequency of small radial oscillations of a spherical liquid drop is…

PHYSICS · Subjective · CBSE · Physics · Units and Measurements · Units and Measurements

Problem

The angular frequency

\omega

of small radial oscillations of a spherical liquid drop is hypothesised to follow the relation

\omega = k\sqrt{\dfrac{S}{\rho r^{3}}},

where

S

is the surface tension of the liquid,

\rho

its density, and

r

the radius of the drop. (a) Verify that the equation is dimensionally homogeneous. (b) Hence determine the dimensions of the constant

k

. (c) If for water (

S = 7.2\times10^{-2}\,\text{N\,m}^{-1}

\rho = 1.0\times10^{3}\,\text{kg\,m}^{-3}

) a drop of radius

1.0\,\text{mm}

is observed to oscillate with

\omega = 1.9\times10^{4}\,\text{s}^{-1}

, calculate the numerical value of

k