A stationary particle breaks into two parts of masses mₐ and mᵦ which move with velocities vₐ and vᵦ respectively. The ratio of their kinetic energies (Kᵦ : Kₐ) is :
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A stationary particle breaks into two parts of masses mₐ and mᵦ which move with velocities vₐ and vᵦ respectively. The ratio of their kinetic energies (Kᵦ : Kₐ) is :

G1 Physics · Accepted Answer

Initial momentum is zero. Hence the two fragments have equal and opposite momenta: mₐvₐ = mᵦvᵦ Kinetic energy can be written as: K = p²/(2m) For equal momentum magnitude: K ∝ 1/m Also from momentum conservation: mₐ/mᵦ = vᵦ/vₐ Therefore: Kᵦ/Kₐ = mₐ/mᵦ = vᵦ/vₐ Hence: Kᵦ : Kₐ = vᵦ : vₐ