A particle is moving with constant speed V `m//s` along the circumference of a circle of radius R meters as shown. A, B and C are three points on periphery of the circle and `DeltaABC` is equilateral. The magnitude of average velocity of particle, as it moves from A to C in clockwise sence, will be :

Options

A. `(3V)/(2pi)`
B. `(3V)/(4pi)`
C. `(3sqrt(3)V)/(2pi)`
D. `(3sqrt(3)V)/(4pi)`

Answer

D

Explanation

A particle …………..
The displacement of particle from A to C will be
`Rxx2 cos 30 implies sqrt(3)R`
Time taken in moving from A to C will be
`(A to C"distance")/(V) implies (4pi R)/(3V)`

`:. V_(av)= (sqrt(3)R)/((4piR)/(3V)) = (3sqrt(3)V)/(4pi)`