Question

A particle moves uniformly in a circular path of radius 10 m. It takes 10 s to complete one revolution. Its speed after 20 s will be-

• A. 1 m/s
• B. \(2\pi\) m/s
• C. 0
• D. \(\pi\) m/s

Hint:

In uniform circular motion, speed remains constant but velocity changes continuously because the direction changes at every point.

Answer 1

The Correct Option is B

Concept: For uniform circular motion, \[ \text{Speed}=\frac{\text{Distance travelled in one revolution}}{\text{Time period}} \] and the distance travelled in one revolution is the circumference of the circle.

Step 1: Calculate the circumference of the circular path.
Given radius, \[ r=10\text{ m} \] Circumference of the circle, \[ =2\pi r =2\pi(10) =20\pi \text{ m} \]

Step 2: Find the speed of the particle.
Time period, \[ T=10\text{ s} \] Therefore, \[ v=\frac{20\pi}{10} =2\pi \text{ m/s} \]

Step 3: Determine the speed after 20 seconds.
The motion is uniform circular motion, so speed remains constant throughout. Hence even after 20 seconds, \[ v=2\pi \text{ m/s} \] \(2\pi\) m/s