Question

A body moves along a circular path of diameter \(30 \text{cm}\). It starts from one end of diameter, moves along the circular path and reaches the other end of diameter in 3 second. The angular speed of the body in radian per second is

• A. \(\frac{π}{5}\)
• B. \(\frac{π}{4}\)
• C. \(\frac{π}{3}\)
• D. \(\frac{π}{2}\)

Hint:

A trip between ends of a diameter covers an angle of pi radians.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Angular speed is the angle swept divided by the time taken: \(\omega = \frac{\theta}{t}\).

Step 2: Key Formula or Approach:
The body goes from one end of a diameter to the other, which is half of a circle. The angle swept is \(\pi\) radians.

Step 3: Detailed Explanation:
\[ \omega = \frac{\pi}{3}\ \text{rad/s} \]
The diameter of \(30\) cm is extra information. The angular speed does not depend on the radius.
The values \(\frac\pi5\), \(\frac\pi4\) and \(\frac\pi2\) would correspond to times of \(5\) s, \(4\) s and \(2\) s.

Final Answer:
The angular speed is \(\frac{\pi}{3}\) rad/s, option (C). \[ \boxed{\frac{\pi}{3}\ \text{rad/s}} \]