The ratio of angular speeds of second hand and minute hand of a watch is

The correct option is B $60:1$
We know that, a second hand takes $1\text{min}$ for one complete cycle and the minute hands takes $60\text{min}$ for one complete cycle, and we know,
$\omega =\frac{2\times \pi }{T}$
So, ${\omega }_{min}=\frac{2\pi }{60}\frac{\text{rad}}{\text{min}}$

${\omega }_{sec}=\frac{2\pi }{1}\frac{\text{rad}}{\text{min}}\Rightarrow \frac{{\omega }_{sec}}{{\omega }_{min}}=\frac{\frac{2\pi }{1}}{\frac{2\pi }{60}}=60:1$
Hence option (b) is the correct answer.