A stationary particle explodes into two particles of masses

Home » Mechanics » Work, Energy and Power » Question

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. m₁v₂/m₂v₁
2. m₂/m₁
3. m₁/m₂
4. 1

Correct Option: B

From conservation law of momentum, before collision and after collision linear momentum (p) will be same. That is,
initial momentum = final momentum.
⇒ 0 = m₁v₁ – m₂v₂ ⇒ m₁v₁ = m₂v₂
p₁ = p₂

E =	p²
	2m

∴	E₁	=	p₁²	×	2m₂
	E₂		2m₁		p₂²

⇒	E₁	=	m₂	[p₁ = p₂]
	E₂		m₁