A particle is moving with constant speed in a circular path. When the particle turns by an angle 90 ° , the ratio of instantaneous velocity to its average velocity is π : x 2 . The value of x will be

Step-by-step solution

In circular motion with constant speed, magnitude of instantaneous velocity, v i n s = ω r . Time taken to turn by 90 ° will be = π 2 ω = π 2 ω . Displacement will be equal to the length of A B = r 2 + r 2 = r 2 Average velocity v a v g = displacement time = r 2 × 2 ω π = 2 2 π ω r Hence, required ratio v ins  v avg  = ω r π 2 2 ω r = π 2 2 Therefore, x = 2 .