Question

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

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

Answer 1

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

$2minutes20seconds=2\times 60+20=120+20=140s=40\times 3+20s$

After $2minutes20seconds$ the particle has completed 3 revolutions and a half revolution,therefore is at the other end of the diameter.

Displacement=$2r$

Distance covered =$3\times 2\pi r+\pi r=7\pi r$

$\frac{\mid displacement\mid }{distance}=\frac{2r}{7\pi r}=\frac{2}{7\pi }$