If the radius of curvature of the path of two particles of same mass are in the ratio 3: 4, then in order to have constant centripetal force, their velocities will be in the ratio of :

Solution

Physics sir · 3 steps

Same mass and same force means v² must grow in step with r, so v goes as √r.

1. Centripetal force. A particle moving on a curve of radius r with speed v needs a force toward the centre of F = mv²/r.
2. Fix F and m. Both F and m are the same for the two particles, so v²/r must be the same too. That means v² ∝ r, or v ∝ √r.

   v₁/v₂ = √(r₁/r₂) = √(3/4) = √3/2

3. So. The velocities are in the ratio √3 : 2, which is option (c).

The idea to keep. For a fixed centripetal force on a fixed mass, v ∝ √r: a wider curve needs a higher speed. Write the formula, hold the fixed quantities constant, and read off the proportionality.

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