Question

A sphere rolls without sliding on a rough inclined plane (only mg and contact forces are acting on the body). The angular momentum, of the body:

• A. about centre is conserved
• B. is conserved about the point of contact
• C. is conserved about a point whose distance from the inclined plane is greater than the radius of the sphere
• D. is not conserved about any point

Answer 1

The correct option is A about centre is conserved

Given: A sphere rolls without sliding on a rough inclines plane (only mg and contact forces are acting on the body).

To find the angular momentum, of the body

Solution:

The required angular momentum of the body is

$L=I\omega +r\times mv⟹L=\frac{2}{5}m{r}^2\times \frac{v}{r}+mvr⟹L=\frac{7}{5}mvr$

and it is about the center and is conserved