Question

A stationary particle explodes into two particles of masses m1 and m2 which move in opposite directions with velocity v1 and v2 the ratio of the kinetic energy is given by key to is

Answer 1

Thank you for asking this question. Here is your answer:

First of all we will solve this equation.

E₁/E₂ = 1/2 m₁v₁²/ 1/2m₂v₂²

= p²₁/2m₁/ P²₂/ 2m₂

= m₂/m₁

If there is any confusion please leave a comment below..

Answer 2

The final momentum after explosion is equal to the initial momentum(from the law of conservation of energy).

Thus, m₁v₁ + m₂v₂ = (m₁+m₂)V

As initially the particle was static, V = 0 and as v₁ and v₂ is opposite in direction,

m₁v₁ - m₂v₂ = 0

or, m₁v₁ = m₂v₂

or, (m₁v₁)² = (m₂v₂)²

or, (1/2)m₁²v₁² = (1/2)m₂²v₂²

or, E₁.m₁ = E₂.m₂

or, E₁ / E₂ = m₂ / m₁