Two nuclei have mass number in the ratio 1:27, then the ratio of their radii and densities should be respectively

1 : 3 and 1 : 1

We know, Radius of Nucleus \( R \propto A^{1 / 3} \)

Where A is mass number

∴ \(\frac{R_1}{R_2} = \left(\frac{1}{27}\right)^{\frac{1}{3}} = \frac{1}{3}=1: 3 \)

While nuclear density is same for all nuclei 

$ \rho = \frac{M}{V} = \frac{m_p A}{\frac{4\pi }{3} r^3} = \frac{3m_p A}{4\pi  k A} = \frac{3m_p }{4\pi k}$

$ \rho$ is independent of A.

∴ \( \frac{\rho_1}{\rho_2}=1: 1 \)