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NTA Abhyas JEE Main2020PhysicsCenter of Mass, Momentum and CollisionPractice

A neutron collides elastically with the stationary nucleus of an atom of mass number A . If the collision is perfectly elastic, then after the collision the fraction of the initial kinetic energy retained by the neutron, is

Options

  1. A1 - A A + 1 2
  2. BA + 1 A - 1 2
  3. CA - 1 A 2
  4. DA + 1 A 2

Correct answer

A. 1 - A A + 1 2

Step-by-step solution

Let us assume the mass of the neutron is m n = m and mass of the nucleus is m A = A m Also, let us assume that the initial and the final velocities of the neutron are v i and v f respectively. Using the formula of final velocity for a perfectly elastic collision we get, v f = m - A m ( m + A m ) v i = 1 - A 1 + A v i ⇒       v f v i = 1 - A 1 + A ⇒ K f i n a l K i n i t i a l = 1 - A 1 + A 2

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