Question

The angular momentum of a hollow sphere of radius R about an axis, passing through its centre of mass perpendicular to the plane and rotating with an angular velocity $\omega$ will be:

• A. $\left(2m{R}^2/5\right)\omega$
• B. $\left(m{R}^2/2\right)\omega$
• C. $\left(2m{R}^2/3\right)\omega$
• D. $\left(m{R}^2/3\right)\omega$

Answer 1

The correct option is C $\left(2m{R}^2/3\right)\omega$

The centre of mass of the sphere passes through the centre of the sphere and the axis is the diameter.
Moment of inertia of a hollow sphere about the diameter is $2m{R}^2/3$
The angular momentum is given be $I\omega =\left(2m{R}^2/3\right)\omega$
The correct option is (c)