A and B are moving in 2 circular orbits with angular velocity 2ω and ω respectively. Their positions are as shown at t = 0. Find the time when they will meet for first time.

Case-1: When they rotate in same sense 2mπ=2ωt3π2+2nπ=ωt2mπ=23π2+2nπ2m=3π+4nm=32+2n⇒ m−2n=32Not possible as m and n are integers. Case-2: When they rotate in opposite sense 2mπ=2ωtπ2+2nπ=ωt2mπ=2π2+2nπ2mπ=π+4nπ2m−4n=1Not possible as m and n are integer.