Question

$\text{Statement 1:}$ A rigid disc rolls without slipping on a fixed rough horizontal surface with uniform angular velocity, then the acceleration of the lowest point on the disc is zero.

$\text{Statement 2:}$ For a rigid rolling without slipping on a fixed rough horizontal surface, the velocity at the lowest point on the disc is always zero.

• A. Statement $1$ is false and statement $2$ is true.
• B. Statement $1$ is true and statement $2$ is false.
• C. Both statements are true and statement $2$ is the correct explanation of statement $1$.
• D. Both statements are true and statement $1$ is the correct explanation of $2$.

Answer 1

The correct option is A Statement $1$ is false and statement $2$ is true.

For a disc rolling without slipping, translation part of rolling produce zero acceleration at the lowest point. But rotational part of rolling creates zero tangential acceleration and non- zero centripetal acceleration which will be in upward direction.

So, for a disc rolling without slipping on a horizontal rough surface with uniform angular velocity, the acceleration of the lowest point is directed upward and not zero.

Hence, statement $1$ is false while velocity of the lowest point is always zero. So the statement $2$ is true.

Therefore, option $\left(\text{A}\right)$ is correct.

Why this question? In pure rolling motion, keep in mind that velocity of the lowest point of the object is always zero and velocity of other points can be calculated with respect to the stationary point.