Question

A solid sphere is pushed on a horizontal surface such that it slides with a speed 3.5 m/s initially without rolling. The sphere will start rolling without slipping when its velocity becomes:

• A. 2.5 m/s
• B. 5 m/s
• C. 3.5 m/s
• D. 7 m/s

Hint:

When an object transitions from sliding to rolling, its velocity must satisfy the rolling condition \( v = r\omega \).

Answer 1

The Correct Option is A

For rolling motion without slipping, the condition is that the linear velocity must match the angular velocity condition. Using the relation between sliding and rolling velocity, we find that the velocity at which the sphere starts rolling is 2.5 m/s. Thus, the correct answer is option (1).