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. $\frac{59\pi }{24000}rad/s$
• D. $\frac{59\pi }{3600}rad/s$

Answer 1

The correct option is B. $\frac{59\pi }{1800}rad/s$.

Step 1,

Time taken by minute hand to rotate by an angle of $2\pi$ radian,

$t_m=1$ hr $=3600$ seconds

$\therefore$ Angular velocity of minute hand

${\omega }_m=\frac{2\pi }{3600}rad/s$

Step 2,

Time taken by second hand to rotate by an angle of $2\pi$ radian,

$t_s=1$ minute $=60$ seconds

$\therefore$ Angular velocity of second hand

${\omega }_s=\frac{2\pi }{60}rad/s$

Step 3,

$\therefore$ ${\omega }_s-{\omega }_m=\frac{2\pi }{60}-\frac{2\pi }{3600}=\frac{59\pi }{1800}$ $rad/s$.

Hence the difference between the angular speed is $\frac{59\pi }{1800}$ rad/sec