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Q55 (NDA-I/2023) Science & Technology › Basic Science (Physics, Chemistry, Biology) Official Key

A particle is moving in a circle of radius R with a constant speed v. Its average acceleration over the time when it moves over half the circle is :

Explanation

Average acceleration is defined as the total change in velocity divided by the total time taken. For a particle moving in a circle of radius R with a constant speed v:

  • Time Interval (t): To cover half the circumference of the circle (distance = Ï€R), the time taken is t = Ï€R / v.
  • Change in Velocity (Δv): Velocity is a vector quantity. If the initial velocity at the start of the half-circle is v, then after moving half-way around the circle, the particle moves in the exactly opposite direction with velocity -v. The magnitude of the change in velocity is |v - (-v)| = 2v.
  • Average Acceleration: It is calculated as Δv / t = 2v / (Ï€R / v) = 2v² / Ï€R.

In the given options, T represents the mathematical constant π. Therefore, the average acceleration is 2v² / TR, making Option C correct.

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