Question

The difference between angular speed of minute hand and second hand of a clock is

• A. $\frac{59\pi }{900}rad/s$
• B. $\frac{59\pi }{1800}rad/s$
• C. $\frac{59\pi }{2400}rad/s$
• D. $\frac{59\pi }{3600}rad/s$

Answer 1

Answer: (B)

Angular speed of minute hand,
${\omega }_m=360^{\circ }\text{ per hour }$
$=\left(360\times \frac{\pi }{180}\right)\text{ per hour }=\frac{2\pi }{3600}rad/s$
$\left[\because 1^{\circ }=\frac{\pi }{180}rad\text{ and }1\text{ hour }=3600s\right]$
Angular speed of second hand,
${\omega }_s=360^{\circ }$ per minute $=\frac{2\pi }{60}rad/s$
$\therefore$ Difference between angular speeds of minute hand and second hand of a clock
$={\omega }_m-{\omega }_s=\frac{2\pi }{3600}-\frac{2\pi }{60}=-\frac{59\pi }{1800}$
So, difference between ${\omega }_m$ and ${\omega }_s$ is $\frac{59\pi }{1800}rad/s$