Question

What is the angle (in circular measure) between the hour hand and the minute hand of a clock when the time is half past $4$?

• A. $\frac{\pi }{3}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{6}$
• D. None of the above

Answer 1

The correct option is B $\frac{\pi }{4}$

In the clock the angle between each hour division will be $\frac{360}{12}={30}^o$.

Now here at $4:30$, the hour hand will be along AB which is the angle bisector between $4$ and $5$ and the minute hand will be along AC,

The angle between them will be $=30+15=45$,in radians $\frac{\pi }{4}$

Hence, B is correct.