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: Find the period:
Half a revolution takes $3$ s, so a full revolution takes $T = 6$ s.

Step 2: Use $\omega = 2\pi/T$:
$\omega = \frac{2\pi}{6} = \frac\pi3$ rad/s.

Final Answer:
$\omega = \frac{\pi}{3}$ rad/s, option (C). \[ \boxed{\frac{\pi}{3}\ \text{rad/s}} \]