Question

An ice cube can slide around the inside of a vertical circular hoop of radius . It undergoes small-amplitude oscillations if displaced slightly from the equilibrium position at the lowest point.Find an expression for the period of these small-amplitude oscillations.Give your answer in terms of R and constants g and pi.

Answer 1

Answer:

$T=2\pi \times \sqrt {\frac {g}{\mu R}$

Explanation:

$\mu mw^{2}R=mg$

where m is the mass, g is acceleration due to gravity

The masses m are on both sides hence they cancel

$W=\sqrt {\frac {g}{\mu R}$

We know that T=2\pi W and substituting W with the above equation then

$T=2\pi \times \sqrt {\frac {g}{\mu R}$