Question

The ratio of the angular speed of minutes hand and hour hand of a watch is:

• A. $6:1$
• B. $12:1$
• C. $1:6$
• D. $1:12$

Answer 1

The correct option is B $12:1$

Time taken by minute hand to rotate by $2\pi$ radian angle is $60$ minute $=3600$ $s$

$⟹$ Angular speed of minute hand $w_m=\frac{2\pi }{3600}=\frac{\pi }{1800}$ $rad/s$

Time taken by hour hand to rotate by $2\pi$ radian angle is $12$ hrs $=43200$ $s$

$⟹$ Angular speed of minute hand $w_h=\frac{2\pi }{43200}=\frac{\pi }{21600}$ $rad/s$

$\therefore$ $\frac{w_m}{w_h}=\frac{\frac{\pi }{1800}}{\frac{\pi }{21600}}=12$

$⟹$ $w_m:w_h=12:1$