Question

A body is traveling in a circle of radius 10 cm as shown. What is the ratio of the average speed to the average velocity when it reaches N from M in a clockwise direction along the circumference of the circle in 1 min?

• A. $\frac{\pi }{2\sqrt{2}}$
• B. $\frac{\pi }{4}$
• C. $\frac{1}{2\sqrt{2}}$
• D. $\sqrt{2}$

Answer 1

The correct option is A $\frac{\pi }{2\sqrt{2}}$


$\text{Displacement of the body}=\text{MN (straight line)}=\sqrt{{10}^2+{10}^2}=10\sqrt{2}cm$
$\text{Distance covered by the body}=MN\left(arc\right)=1/4\times 2\pi r=5\pi cm$

$\text{Average speed, s}=\frac{Distance}{Time}=\frac{5\pi }{60}=\frac{\pi }{12}cm/s$
$\text{Average velocity, v}=\frac{Displacement}{Time}=\frac{10\sqrt{2}}{60}=\frac{\sqrt{2}}{6}cm/s$
$\text{Ratio of average speed to average velocity}=\frac{s}{v}=\frac{\pi }{2\sqrt{2}}$