Let ω_1, ω_2 and ω_3 be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If x_1, x_2…

Let $\displaystyle \omega_1, \omega_2$ and $\displaystyle \omega_3$ be the angular speed of the second hand, minute hand and hour hand of a smoothly running analog clock, respectively. If $\displaystyle x_1, x_2$ and $\displaystyle x_3$ are their respective angular distances in $\displaystyle 1$ minute then the factor which remains constant $\displaystyle (k)$ is