An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8: 27 . The ratio of the radii of the nuclei (assumed to be spherical ) is:

Step-by-step solution

Let heavy nucleus breaks into two nuclei of mass m₁ and m₂ and move away with velocities V₁ and V₂ respectively. According to question, V₁ V₂ = 8 27 m₁ V₁=m₂ V₂ (Law of momentum conservation) aligned & m₁ m₂ = V₂ V₁ = 27 8 & 4 3 R₁^3 4 3 R₂^3 ( density = mass volume ) aligned aligned & ( R ₁ R ₂ )= ( 27 8 )^ 1 3 = ( 3 2 )^ 3 1 3 & R ₁ R ₂ = 3 2 aligned