Question

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

• A. $6:1$
• B. $12:1$
• C. $60:1$
• D. $1:60$

Answer 1

Answer: (B)

${\omega }_{mh}=$ Angular speed of minute hand
${\omega }_{hh}=$ Angular speed of hour hand
${\omega }_{mh}=\frac{2\pi }{60m}=\frac{2\pi }{60\times 60}rad{s}^{-1}$
${\omega }_{hh}=\frac{2\pi }{12h}=\frac{2\pi }{12\times 60\times 60}rad{s}^{-1}$
$\frac{{\omega }_{mh}}{{\omega }_{hh}}=\frac{\frac{2\pi }{60\times 60}}{\frac{2\pi }{12\times 60\times 60}}=\frac{1}{1}\times \frac{12}{1}$
${\omega }_{mh}:{\omega }_{hh}\Rightarrow 12:1$