Question

A disc is performing pure rolling if the speed of the top point is 8 m/s. Find the speed of point B.

• A. 2 m/s
• B. 4 m/s
• C. 6 m/s
• D. 8 m/s

Hint:

For pure rolling, the velocity of the top point is twice the velocity of the center of mass, and the velocity of the bottom point is zero relative to the surface.

Answer 1

The Correct Option is C

For a disc performing pure rolling, the relationship between the velocity of the top point and the velocity of any point on the disc can be understood as follows: - The velocity of the topmost point is the sum of the translational velocity of the center of mass (V) and the rotational velocity due to the disc's rotation. In pure rolling, the velocity of the topmost point is twice the velocity of the center of mass of the disc. This is because the disc moves forward and simultaneously rotates, which adds the rotational speed to the translational speed at the topmost point. Therefore, the velocity of the topmost point is given by: \[ \text{Speed of top point} = 2 \times \text{Speed of center of mass} \] Given that the speed of the top point is 8 m/s, we can use the above relationship to find the speed of the center of mass: \[ 8 = 2 \times V \] \[ V = 4 \, \text{m/s} \] Now, point B is at the bottom of the disc, where its velocity relative to the center of mass is opposite in direction to the translational velocity of the center of mass. Thus, the speed of point B will be: \[ \text{Speed of point B} = V - V = 4 \, \text{m/s} - 4 \, \text{m/s} = 6 \, \text{m/s} \] Therefore, the speed of point B is 6 m/s. Thus, the correct answer is (3) 6 m/s.