Question

A coin placed on a gramophone record rotating at $33\text{rpm}$ flies off record, if it is placed at a distance of more than $16\text{cm}$ from the axis of rotation. If the record is revolving at $66\text{rpm}$, the coin will fly off if is placed at a distance( in $\text{cm}$) not less than

Answer 1

Here friction provides necessary centripetal force so
$\mu mg=mr{\omega }^2$
$\mu$ and g are constans.
$\therefore r{\omega }^2$ = constant
$r^{\prime }=\frac{r{33}^2}{{66}^2}$
$r^{\prime }=\frac{r}{4}=\frac{\text{16 cm}}{4}=\text{4 cm}$