Question

The acute angle between the hour hand and minute hand of a clock when the time is $5hours$ and $40minute$ is

• A. $\frac{\pi }{2}$
• B. $\frac{13\pi }{36}$
• C. $\frac{5\pi }{18}$
• D. $\frac{7\pi }{18}$

Answer 1

Answer: (D)

For minute hand 60 minutes =$360^{\circ }$
40 minutes = $\frac{360^{\circ }}{60}\times 40=240^{\circ }$ and for hour hand
1 hr = 60 minutes = $30^{\circ }$
40 minutes = $\frac{30^{\circ }}{60}\times 40=20^{\circ }$
$\therefore$ For 5 hr 40 min.= $30^{\circ }\times 5+20^{\circ }=170^{\circ }$.
Hence, required angle = $240^{\circ }-170^{\circ }=70^{\circ }$
$=70^{\circ }\times \frac{\pi }{180^{\circ }}=\frac{7\pi }{18}$