:) The ratio of angular speed of a second-hand to the hour - hand of a

1.	:) The ratio of angular speed of a second-hand to the hour - hand of a watchesa) 60: 1b) 72: 1c) 720:1d) 3600:1
Answer» $\huge\underline{\underline{\bf \orange{Question-}}}$ The RATIO of angular speed of a second-hand to the hour - hand of a watches. $\huge\underline{\underline{\bf \orange{Solution-}}}$ We know that , In watch's second hand it takes 1 min (60s) to COMPLETE one Angular distance i.e 2π So , $\implies{\sf Angular\:Speed(\omega_1)=\dfrac{2π}{60}}$ $\implies{\sf \pink{ \omega_1 = \dfrac{π}{30}\:rad/s}}$ And , Hour hand to watch take 12 HOURS (12×3600=43200s) to complete one rotation i.e 2π $\implies{\sf Angular\:Speed(\omega_2)=\dfrac{2π}{43200} }$ $\implies{\sf \pink{\omega_2= \dfrac{π}{21600} \:rad/s}}$ $\large{\rm Ratio \: of \: second-hand \: and \:hour-hand }$ $\implies{\sf \dfrac{\omega_1}{\omega_2}=\dfrac{π/30}{π/21600} }$ $\implies{\sf \dfrac{\omega_1}{\omega_2}=\dfrac{<klux>720</klux>}{1}}$ $\implies{\bf \red{\omega_1:\omega_2=720:1} }$ $\huge\underline{\underline{\bf \orange{Answer-}}}$ Option (c) 720 : 1 Ratio of angular speed of a second-hand to the hour - hand of a watches is ${\bf \red{720:1}}$ .