Question

A particle is moving along a circle such that it completes one revolution in $40$ seconds. In $2$ minutes $20$ seconds, the ratio $\frac{\left|displacement\right|}{distance}$ is

• A. $0$
• B. $\frac{1}{7}$
• C. $\frac{2}{7}$
• D. $\frac{7}{11}$

Answer 1

The correct option is C $\frac{2}{7}$

Particle completes revolution in $40$ seconds.

$20$ minutes $20$ second $=140$ second

$=40\times 3+20$ second

Therefore, the player would have completes $3.5$ revolutions.

$\therefore$ Distance $=3\times 2\pi r\times \pi r=7\pi r$

where as, Displacement $=2r$ (the other end of the diameter)

$\therefore \frac{|Displacement|}{Distance}=\frac{2r}{7\pi r}=\frac{2}{7\pi }$