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Question

Physics Question on Motion in a plane

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

A

421π11600\frac {421π}{11600}

B

19π15600\frac {19π}{15600}

C

719π21600\frac {719π}{21600}

D

311π57800\frac {311π}{57800}

Answer

719π21600\frac {719π}{21600}

Explanation

Solution

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 = 2π radians60 seconds\frac {2π \ radians}{60 \ seconds}= π30\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 = 2π radians43200 seconds\frac {2π \ radians}{43200 \ seconds} = π21600\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 = π30−π21600\frac {π}{30}-\frac {π}{21600} = 719π21,600\frac {719π}{21,600} radians per second
Therefore, the correct answer is: 719π21,600\frac {719π}{21,600}