Question

A uniform solid sphere of radius R, rolling without sliding on a horizontal surface with an angular velocity ${\omega }_0$, meets a rough inclined plane of inclination $\theta ={60}^{\circ }$.The sphere starts pure rolling up the plane with an angular velocity $\omega$ . Find the value of $\omega$.

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Using the conservation of angular momentum about the point of contact with the inclined plane.

$\frac{2}{5}m{R}^2{\omega }_0+m{v}_{0}Rcos{60}^{\circ }=\frac{7}{5}m{R}^2\omega \Rightarrow \frac{2}{5}m{R}^2{\omega }_0+\frac{m{\omega }_0{R}^2}{2}=\frac{7}{5}m{R}^2\omega$

$\Rightarrow \frac{9}{10}m{R}^2{\omega }_0=\frac{7}{5}m{R}^2\omega \therefore \omega =\frac{9}{14}{\omega }_0$