Question

The acute angle in radians between the minute and the hour hand of a clock when the time is $4$ hours $20$ minutes is:

• A. $\pi /18$
• B. Zero
• C. $\pi /6$
• D. $\pi /9$

Answer 1

The correct option is A $\pi /18$

Solution:

Every $5$ seconds measures angle $\frac{360}{60}\times 5$ and $20$ minutes is $\frac{1}{3}$rd of $60$ minutes

The acute angle between the minute and the hour hand of a clock when the time is $4$ hours and $20$ minutes $=\frac{1}{3}\times {30}^{\circ }=\frac{1}{3}\times \frac{\pi }{6}=\frac{\pi }{18}$

Hence, A is the correct option.