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

Step 1: Note the given values.
Radius of the circle is $r = 10$ m. Time for one full round is $T = 10$ s. We want the speed after 20 s.

Step 2: Recall what speed means here.
Speed is distance covered divided by time taken. In one round the particle covers the full boundary of the circle.

Step 3: Find the distance in one round.
The boundary of a circle is its circumference. \[ \text{Circumference} = 2\pi r = 2\pi (10) = 20\pi \text{ m} \]

Step 4: Find the speed.
The particle covers $20\pi$ m in $10$ s. \[ v = \frac{20\pi}{10} = 2\pi \text{ m/s} \]

Step 5: Think about "uniform" motion.
The word uniform means the speed never changes. It stays the same at every moment.

Step 6: Answer for 20 s.
Since the speed does not change, after 20 s it is still the same value. \[ \boxed{2\pi \text{ m/s}} \]