Question

A sphere is released on a smooth inclined plane from the top. When it moves down, its angular momentum is

• A. conserved about every point
• B. conserved about the point of contact only
• C. conserved about the centre of the sphere only
• D. conserved about any point on a line parallel to the inclined plane and passing through the centre of the ball

Answer 1

The correct option is D conserved about any point on a line parallel to the inclined plane and passing through the centre of the ball

As $\frac{dL}{dt}=\tau$

For $L$ to be conserved, net torque about that point must be zero.

$N=mgcos\alpha$

Thus net external force on the ball, $F_{external}=mgsin\alpha$

Now ${\tau }_A=0$ due to $F_{external}$

Hence, $L$ is conserved about any point on a line paralell to the inclined plane and passing through the centre of the ball.