The ratio of angular speed of a second-hand to the hour-hand of a watch is

The correct option is A $720:1$
Time taken by second-hand to rotate by $2\pi$ radian $t=60$ s

Angular velocity of second-hand $w_s=\frac{2\pi }{60}$ $rad/s$

Time taken by hour-hand to rotate by $2\pi$ radian $t=12$ hr $=43200$ s

Angular velocity of hour-hand $w_h=\frac{2\pi }{43200}$ $rad/s$

$⟹$ $\frac{w_s}{w_h}=\frac{43200}{60}=720$