Physics - Modern Physics Question with Solution | TestHub

Density of nuclear matter is independent of mass number, so the required ratio is $1:1$. Alternative $$A_1:A_2=1:3$$ Their radii will be in the ratio $$\begin{array}{r}{R}_0{A}_1^{1/3}:R_0{A}_2^{1/3}=1:3^{1/3}\\ \text{ Density }=\frac{A}{\frac{4}{3}\pi R^3}\\ \therefore {\rho }_{A_1}:{\rho }_{A_2}=\frac{1}{\frac{4}{3}\pi R_0^3\cdot 1^3}=\frac{3}{\frac{4}{3}\pi R_0^3{\left(3^{1/3}\right)}^3}\end{array}$$ Their nuclear densities will be the same.