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))/4 sqrt(65) m/s^(2)`
B. `(pi^(2))/2 sqrt(7) m/s^(2)`
C. `(pi^(2))/3sqrt(15) m/s^(2)`
D. `(pi^(2))/4 sqrt(7) m/s^(2)`

Explanation

At time t=1 sec
`vec(a)_(B)=omega_(2)^(2)r_(2)(-hati)=2pi^(2)(-hati)`
`vec(a)_(A)-vec(a)_(B)=(pi^(2))/4(-hatj)+2pi^(2)(hati)`
`a_(rel)pi^(2)[1/16+4]^(1//2)=(pi^(2))/4sqrt(65)m/s^(2)`