Question

The difference between angular speed of minute hand and second hand of a clock is (in rad/s)

• A. \(\frac{59\pi }{900}\)
• B. \(\frac{59\pi }{1800}\)
• C. \(\frac{59\pi }{2400}\)
• D. \(\frac{59\pi }{3600}\)

Hint:

Angular speed is 2 pi divided by the time period. The minute hand takes 3600 s and the second hand takes 60 s.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The angular speed of a rotating hand is \(\omega=\dfrac{2\pi}{T}\).

Step 2: Minute Hand
\(T=3600\) s, so \(\omega_m=\dfrac{2\pi}{3600}=\dfrac{\pi}{1800}\) rad/s.

Step 3: Second Hand
\(T=60\) s, so \(\omega_s=\dfrac{2\pi}{60}=\dfrac{60\pi}{1800}\) rad/s.

Step 4: Difference
\(\omega_s-\omega_m=\dfrac{60\pi-\pi}{1800}=\dfrac{59\pi}{1800}\) rad/s.

Final Answer:
The difference in angular speeds is 59 pi over 1800 rad/s. \[ \boxed{\text{(B) }\dfrac{59\pi}{1800}} \]