Question

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 m/s. The speed of the particle on the rim of the wheel at the same level as the center of the wheel, will be:

• A. \( 4\sqrt{2} \, \text{m/s} \)
• B. 8 m/s
• C. 4 m/s
• D. \( 8\sqrt{2} \, \text{m/s} \)

Hint:

The speed of a point on the rim of a rolling wheel is the sum of the translational speed and the rotational speed. At the highest point, these speeds add up.

Answer 1

The Correct Option is A

Given that the speed of the particle at the highest point of the rim is 8 m/s, and the wheel is rolling without slipping, the speed at any point on the rim is the sum of the velocity of the center of the wheel and the velocity due to the rotational motion. 

Let: 
- \( V_B = 8 \, \text{m/s} \) (speed at the highest point of the rim), 
- \( V = 4 \, \text{m/s} \) (speed of the center of the wheel), 
- \( V_P = \sqrt{2}V \) (velocity at point \( P \)). 

Since the wheel is rolling without slipping, the speed at point \( P \) (which is the same level as the center of the wheel) will be: \[ V_P = \sqrt{2} \times 4 = 4\sqrt{2} \, \text{m/s} \] 
Thus, the correct answer is (1).