Question

Assertion :A disc is rolling on an inclined plane without slipping. The velocity of centre of mass is $V$. The other points on the disc lie on a circular arc having same speed as that of the centre of mass. Reason: When a disc is rolling on an inclined plane, the magnitude of velocities of all the points from the contact point is the same, having distance equal to radius $r$.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

As the disc is not slipping, thus velocity of the contact point A must be zero.

$V=rw$ where $r$ is the radius of the disc.

Now the axis passing through the point A and perpendicular to the plane acts as the instantaneous axis of rotation.

Thus the velocity of particle p w.r.t point A, $v_p=rw=V$

Similarly there are some other particles having a velocity $V$ which lie at a distance $r$ from point A. Hence they lie on the circular arc centered at point A.

Thus Reason is the correct explanation of Assertion.