Question

A solid sphere rolls on a smooth horizontal surface at $10m/s$ and then rolls up a smooth inclined plane of inclination ${30}^o$ with horizontal. The mass of the sphere is $2kg$. Find the height attained by the sphere before it stops (in $m$).

Answer 1

Using the energy conservation

we know $\omega r=v=10$

$\frac{m{v}^2}{2}+\frac{1}{2}\frac{2m{r}^2}{5}{\omega }^2=mgh$

$h=7v/10=7m$