Question

A particle is moving with constant speed in a circular path. When the particle turns by angle 90⁰, the ratio of instantaneous velocity to its average velocity is π:x√2. The value of x will be

Answer 1

\(V_A = vj\)

And \(V_B = -vi\)

Time to reach from A to B = \(\frac{2\pi R}{4} \times \frac{1}{v} = \frac{\pi R}{2v}\)

Displacement from A to B = \(\frac{Displacement}{Time}\) = \(\frac{R \sqrt2}{\frac{\pi R}{2v}} = \frac{2\sqrt 2 v}{\pi}\)

Instantaneous velocity at  is \(-v\hat i\)

According to question, \(\frac{instantaneous\, velocity}{average velocity} = \frac{\pi}{x\sqrt2}\)