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A stationary particle explodes into two particles of masses m₁ and m₂ which move in opposite directions with velocities v₁ and v₂. The ratio of their kinetic energies E₁/E₂ is

1. m₂v₁/m₁v₂
2. m₁/m₂
3. m₁²/m₂²
4. 1

Correct answer: m₁²/m₂²

Solution

The kinetic energy of a particle is given by E = (1/2)mv². For the two particles, the ratio of their kinetic energies is E₁/E₂ = (1/2)m₁v₁² / (1/2)m₂v₂² = (m₁v₁²) / (m₂v₂²). Using conservation of momentum, m₁v₁ = m₂v₂, so v₁/v₂ = m₂/m₁. Substituting this into the energy ratio gives E₁/E₂ = (m₁/m₂)².

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