Physics

Problem

The frequency

f

of small vertical oscillations of a uniform solid cylinder of radius

r

floating upright in a liquid of density

\rho

is hypothesised to be

f = C\,\sqrt{\dfrac{g}{\rho r}},

where

g

is the acceleration due to gravity and

C

is a constant. The dimensional formula of

C

is a)

M^{-1/2}L^{3/2}

M^{1/2}L^{-3/2}

M^{1/2}L^{-3/2}T^{1}

M L^{-3}T^{1}