Question

A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8 : 1. The ratio of radii of the fragments is

• A. 1 : 2
• B. 1 : 4
• C. 4 : 1
• D. 2 : 1

Answer 1

Answer: (A)

1 : 2

Answer 2

By conservation of momentum m₁v₁ = m₂v₂

⇒ $\frac{v_{1}}{v_{2}} = \frac{8}{1} = \frac{m_{2}}{m_{1}}$…… (i)

Also from $r \propto A^{1/3}$ ⇒ $\frac{r_{1}}{r_{2}} = \left( \frac{A_{1}}{A_{2}} \right)^{1/3} = \left( \frac{1}{8} \right)^{1/3} = \frac{1}{2}$