Question

Angular velocity of hour hand of a watch is (in rad/s)

• A. \(\frac{\pi }{43200}\)
• B. \(\frac{\pi }{30}\)
• C. \(\frac{\pi }{21600}\)
• D. \(\frac{\pi }{1800}\)

Hint:

The hour hand completes one revolution in 12 hours. Convert the period to seconds and use the angular velocity formula.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Angular velocity is \(\omega=\frac{2\pi}{T}\), where \(T\) is the time for one full revolution.

Step 2: Find the Period
The hour hand takes 12 hours to go once around.
\(T=12\times 60\times 60=43200\ \text{s}\).

Step 3: Calculation
\(\omega=\frac{2\pi}{43200}=\frac{\pi}{21600}\ \text{rad/s}\).

Final Answer:
The angular velocity of the hour hand is pi divided by 21600 rad/s. \[ \boxed{\text{(C) }\dfrac{\pi}{21600}} \]