A nucleus disintegrates into two nuclear parts, which have their velocities in the ratio 2 : 1. The ratio of their nuclear radii will be …

From conservation of linear momentum
m₁V₁ = m₂V₂
A₁V₁=A₂V₂
$\frac{A_1}{A_2}=\frac{V_2}{V_1}=\frac{1}{2}\mathrm{.....}\left(1\right)$ 
For a nucleus, Radius,  R=RoA^1/3
 $$\begin{gathered} R\alpha A^{1/3} \\ \frac{R_1}{R_2}={\left(\frac{A_1}{A_2}\right)}^{1/3}={\left(\frac{1}{2}\right)}^{1/3} \end{gathered}$$