Question

The relative angular speed of hour hand and minute hand of clock is

• A. \(\frac{2π}{60}\)
• B. \(\frac{11π}{360}\)
• C. \(\frac{11π}{21600}\)
• D. \(\frac{2π}{3600}\)

Hint:

Find the angular speed of each hand and subtract.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Both hands rotate in the same direction. The relative angular speed is the difference of their angular speeds.

Step 2: Angular speeds.
The minute hand turns \(2\pi\) rad in 60 min = 3600 s, so \(\omega_m = \dfrac{2\pi}{3600}\) rad/s.
The hour hand turns \(2\pi\) rad in 12 h = 43200 s, so \(\omega_h = \dfrac{2\pi}{43200}\) rad/s.

Step 3: Subtract.
\[ \omega_m - \omega_h = 2\pi\left(\frac{1}{3600} - \frac{1}{43200}\right) = 2\pi\cdot\frac{12 - 1}{43200} = \frac{22\pi}{43200} = \frac{11\pi}{21600}\ \text{rad/s} \]

Step 4: Check the options.
Option (A) is \(2\pi/60\), the minute hand speed in rad per minute. Option (D) is \(2\pi/3600\), the minute hand speed alone. Option (B) has the wrong denominator.

Final Answer:
The relative angular speed is \(\dfrac{11\pi}{21600}\) rad/s, option (C). \[ \boxed{\frac{11\pi}{21600}} \]