Question

The relative angular speed of hour hand and second hand of a clock is (in rad/s)

• A. \(\frac {421π}{11600}\)
• B. \(\frac {19π}{15600}\)
• C. \(\frac {719π}{21600}\)
• D. \(\frac {311π}{57800}\)

Answer 1

The Correct Option is C

To find the relative angular speed of the hour hand and the second hand of a clock, we need to consider the angular speed of each hand individually and then find the difference between them.The second hand completes one full revolution (2π radians) in 60 seconds. 
Therefore, its angular speed is:
Angular speed of second hand = \(\frac {2π \ radians}{60 \ seconds}\)= \(\frac {π}{30}\) radians per second
The hour hand completes one full revolution in 12 hours, which is equivalent to 720 minutes or 43,200 seconds. Since the hour hand has a length that is a fraction of the minute hand, its angular speed is much slower.
Angular speed of hour hand = \(\frac {2π \ radians}{43200 \ seconds}\) = \(\frac {π}{21600}\) radians per second
The relative angular speed can be found by subtracting the angular speed of the hour hand from the angular speed of the second hand:
Relative angular speed = \(\frac {π}{30}-\frac {π}{21600}\) = \(\frac {719π}{21,600}\) radians per second
Therefore, the correct answer is: \(\frac {719π}{21,600}\)

Answer 2

To find the relative angular speed of the hour hand and the second hand of a clock:
- The second hand completes one full revolution (2π radians) in 60 seconds, so its angular speed is:
Angular speed of second hand = \(\frac {π}{30}\) radians per second.
- The hour hand completes one full revolution in 12 hours, equivalent to 43,200 seconds. Its angular speed is:
Angular speed of hour hand = \(\frac {π}{21600}\) radians per second.
- The relative angular speed is found by subtracting the angular speed of the hour hand from the angular speed of the second hand:
Relative angular speed = \(\frac {π}{30} - \frac {π}{21600}\) = \(\frac {719π}{21600}\) radians per second.
Therefore, the correct answer is: \(\frac {719π}{21600}\).