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 -

Solution

Physics sir · 4 steps

Average velocity uses the straight-line chord, but the time comes from the curved arc.

1. Instantaneous velocity. The speed is constant, so the instantaneous velocity has magnitude v at every point on the circle.
2. Displacement and time. For a 90° turn, the start and end points are two radii at right angles. The displacement is the chord joining them, √(R² + R²) = R√2. The particle travels a quarter arc, (π R)/2, so the time taken is t = (π R)/2v.

   v_(avg) = R√2/(π R / 2v) = (2√2 v)/π

3. Take the ratio. v/v_(avg) = v/(2√2 v/π) = π/2√2, so the ratio is π : 2√2.
4. So. Comparing with π : x√2 gives x = 2, which is option (d).

The idea to keep. Average velocity is displacement divided by time. The displacement is the straight chord, and the time comes from the distance actually travelled along the arc.

Answer from the NTA final answer key. Solution by PrepWiser.