Two particles are moving in different circles in same plane with different angular velocities as shown in figure. At t = 0, initial positions of particles A and B are shown by dots on the respective circles. Initial distance between particles is 1m. Particle A move anticlockwise in the first circle whereas B moves clockwise in the second circle. Angle described (rotated) by A and B in time 't' are `theta_(A)=((pi)/2t)` and `theta_(B)=(pit)` respectively. here `theta` is in radian and t is in second. Radius of each circle is shown in diagram.

At time t=2 second, the angular velocity of the particle A with respect to the particle B is

Options

A. `5pi` rad/sec
B. `(3pi)/2` rad/sec
C. `(2pi)/3` rad/sec
D. `(5pi)/6` rad/sec

Explanation

At time t=2 s, position of A and B are `v_(A)=omega_(1)r_(1)=(pi)/2(1)=(pi)/2 m//sec`
`v_(B)=omega_(2)r_(2)=2pi m//sec`.
distance `AB=3m`
`omega=(v_(A)+v_(B))/(AB)=(pi//2+2pi)/3=(5pi)/6 rad//sec`