The ratio of angular speed of minute hand to that of hour hand of a watch is:

The correct option is D $12:1$
$\text{Step 1: Angular speed of hour hand}$

Hour hand makes the rotation of $2\pi$ in $12$ hours.

$\therefore W_H=\frac{2\pi }{12}rad/hr.$ $....\left(1\right)$

$\text{Step 2: Angular speed of minute hand}$

Minute hand makes the rotation of $2\pi$ in $1$ hour.

$\therefore W_M=\frac{2\pi }{1}rad/hr.=2\pi rad/hr.$ $....\left(2\right)$

$\text{Step 3: Ratio of angular speeds}$

Divide equation $\left(1\right)$ & $\left(2\right)$

$\frac{W_M}{W_H}=\frac{2\pi }{\frac{2\pi }{12}}=12:1$

Hence, Option (D) is correct.