Question

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

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

Answer 1

The correct option is C $12:1$

$\begin{array}{cc}60min& ⟶2\pi \\ 1min& ⟶\frac{2\pi }{60}=\frac{\pi }{30}\\ 12h& \to 2\pi \\ 1h& ⟶\frac{2\pi }{12}=\frac{\pi }{6}\\ & \\ 1min& \to \frac{\pi }{6\times 60}=\frac{\pi }{12\times 30}\end{array}$

Now ratio $$\begin{array}{cc}& \Rightarrow \frac{\pi }{30}\times \frac{12\times 30}{\pi }\\ & \Rightarrow 12:1\end{array}$$