The natural frequency (in ) of small radial oscillations of a gas bubble of…

PHYSICS · Single correct · A Level · Physics · Measurements and their errors · Measurements and their errors

Problem

The natural frequency

f

(in

\text{s}^{-1}

) of small radial oscillations of a gas bubble of equilibrium radius

R

in a liquid is believed to depend on the ambient pressure

P

and the density

\rho

of the liquid. Assuming a relation of the form

f \propto P^{a} \rho^{b} R^{c}

, which set of exponents

(a, b, c)

satisfies dimensional consistency? (a)

(\dfrac{1}{2},\, \dfrac{1}{2},\, -1)

(b)

(1,\, -\dfrac{1}{2},\, -1)

(c)

(\dfrac{1}{2},\, -\dfrac{1}{2},\, -1)

(d)

(\dfrac{1}{2},\, -\dfrac{1}{2},\, -\dfrac{1}{2})