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

`T=2\pi * \sqrt {\frac {g}{\mu R}`

Step-by-step 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 * \sqrt {\frac {g}{\mu R}`