Question

The ratio of angular speeds of seconds hand and hour hand of a watch respectively is

• A. 1 : 720
• B. 60 : 1
• C. 1 : 60
• D. 720 : 1

Answer 1

The correct option is D 720 : 1

Angular velocity:- Angular velocity of a particle is the rate at which rotates around a choosen centre point. i.e, rate of change of angle $\left(\Delta \theta /dt\right)$ measured in angle per unit time.

SI unit -radian per sec.

Denoted by $\omega$

So,

$t_s-$ time taken by secons hand to complete one rotation $\left(360°or2\pi radian\right)=60s$

$t_h-$ time taken by hours hand to complete one rotation $\left(360°or2\pi rad\right)=60\times 60\times 12$

So, ${\omega }_s=\frac{2\pi }{60}{\omega }_h=\frac{2\pi }{60\times 60\times 12}$

A/Q

$\frac{{\omega }_s}{{\omega }_h}=\frac{22\pi /60}{2\pi /60\times 60\times 12}=\frac{720}{1}$