The radius of a nucleus varies with its mass number (A) as

The correct answer is Option (3) → directly proportional to cube root of A

All nuclei have almost the same nuclear density, so the volume of a nucleus is proportional to the number of nucleons \( A \).

    \( \displaystyle \frac{4}{3}\pi R^{3} \propto A \;\Rightarrow\; R \propto A^{1/3} \)

In the standard form \( R = R_{0}A^{1/3} \) with \( R_{0} \approx 1.2\times10^{-15}\,\mathrm{m} \), the radius is proportional to the cube root of \( A \).

NCERT (2026-27):
Size of the Nucleus – “… It has been found that a nucleus of mass number A has a radius

    \( \displaystyle R = R_0 A^{1/3} \qquad (13.5) \)

where R₀ = 1.2 × 10⁻¹⁵ m (=1.2 fm; 1 fm = 10⁻¹⁵ m). This means the volume of the nucleus, which is proportional to R³ is proportional to A.”