List I describes four systems, each with two particles A and B in relative motion as shown in figure. List II gives possible magnitudes of their relative velocities (in m s - 1 ) at time t = π 3 s . List-I List-II (I) A and B are moving on a horizontal circle of radius 1 m with uniform angular speed ω = 1 rad s - 1 . The initial angular positions of A and B at time t = 0 are θ = 0 and θ = π 2

Step-by-step solution

(I) Angular velocity of both the particles is same. Therefore, angle between them will remain 90 ° . v r e l = 2 ω R = 2   m   s - 1 Hence, I → S (II) The velocity of A at any time t can be written as v A t = 5 π 2 cos 45 ° i ^ + 5 π 2 × sin 45 ° - g × t j ^ = 5 π 2 i ^ + 5 π 2 - g t j ^ Velocity of B at any time t v B t = - 5 π 2 i ^ + 5 π 2 - g t - 0 . 1 j ^ Relative velocity at time t will be, v → r e l = 5 π i ^ - g × 0