A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be (x/3)¹ᐟ³. The value of x is :

Question

G1 Physics · Accepted Answer

Conservation of momentum gives m₁v₁ = m₂v₂. Since v₁/v₂ = 3/2, m₁/m₂ = 2/3. Nuclear density is approximately constant, so mass ∝ r³. Hence (r₁/r₂)³ = 2/3 and r₁/r₂ = (2/3)¹ᐟ³. Therefore x = 2.