The angular velocity of seconds hand of a watch will be

The correct option is π/30 rad / sec.

Step-by-step Explanation:

To find the angular velocity of the seconds hand of a watch, we use the standard formula for angular velocity:
$\omega =\frac{\theta }{t}$
where:
• $\omega$ is the angular velocity,
• $\theta$ is the angular displacement, and
• $t$ is the time interval.

1. Find the angular displacement ($\theta$):
The seconds hand of a clock completes one full rotation (360 degrees) to complete one cycle. In radians, one full rotation is:
$\theta =2\pi \text{radians}$

2. Find the time taken ($t$):
The time required for the seconds hand to make one complete rotation is 60 seconds (or 1 minute). Therefore:
$t=60\text{seconds}$

3. Calculate the angular velocity ($\omega$):
Substituting these values into the formula:
$\omega =\frac{2\pi \text{rad}}{60\text{sec}}$
Simplifying the fraction by dividing both the numerator and the denominator by 2:
$\omega =\frac{\pi }{30}\text{rad/sec}$

Thus, the angular velocity of the seconds hand of a watch is $\frac{\pi }{30}\text{rad/sec}$.