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  4. A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio ( text displacement / text distance ) is

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

Motion in a Straight Line

Solution:

image
$T=40\, s$
If $t=2$ minute 20 second
$=2 \times 60+20$
$=140\, s$
So, it has completed $3 \frac{1}{2}$ revolution.
Distance travelled $=3 \times 2 \pi R+\pi R$
$=7 \pi R$
Displacement $=2 R$
$\frac{\text { IDisplacement| }}{\text { Distance }}=\frac{2 R}{7 \pi R}$
$=\frac{2}{7 \times \frac{22}{7}}=\frac{1}{11}$