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

Answer

`7`

Explanation

At `t = T//6`, particle will travel only `1//6` of circle.
Average speed
=`(Arc AB)/(Time) = ((2 pi R)//6)/(T//6) = (2 pi R)/(T)`
Average velocity
=`("Chord" AB)/("Time") = (2 R sin 30^@)/(T//6) = (6 R)/(T)`
Difference `=( R)/(T)[(44)/(7) - 6] = (22)/(7 T) = 2 ms^-1` (given)
`R = 7 T = 7 (1) = 7 m`.
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