Q.

A particle is moving in a circle of radius R with constant speed. The time period of the particle is T = 1 s. In a time t = T/6, if the difference between average speed and average velocity of the particle is 2 ms-1, find the radius R of the circle (in meters).

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answer is 7.

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Detailed Solution

At t = T/6, particle will travel only 1/6 of the circle.Average speed =Arc⁡AB Time =(2πR)/6T/6=2πRTAverage velocity = Chord AB Time =2Rsin⁡60∘2T/6=6RTDifference =RT447−6=2R7T=2ms−1( given )R=7T=7(1)=7m
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