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. `(pi^(2))/3 m//s`
B. `(pi^(2))/7`
C. `(pi^(2))/4`
D. None of these

Explanation

At time t=1 s positions of A and B are

Acceleration of A `vec(a)_(A)=omega_(1)^(2)r_(1)(-hatj)=((pi)/2)^(2)(1)(-hatj)`