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JEE Main2014PhysicsMotion in One DimensionActual

A bullet loses 1 n th of its velocity passing through one plank. Considering uniform retardation, the number of such planks that are required to stop the bullet can be:

Options

  1. AInfinite
  2. Bn
  3. Cn 2 2 n - 1
  4. D2 n 2 n - 1

Correct answer

C. n 2 2 n - 1

Step-by-step solution

Let t be the thickness of the plank υ 0 1 - 1 n 2 = υ 0 2 - 2 a t ∴   2 a t = υ 0 2 - υ 0 2 1 - 1 n 2 If m number of planks are required to stop a bullet, then 0 = υ 0 2 - 2 a t m ∴   m = υ 0 2 2 a t = υ 0 2 υ 0 2 1 - 1 - 1 n 2 = n 2 n 2 - n - 1 2 = n 2 2 n - 1

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