JEE Main 2025 Apr 8 Shift 2, Physics Q19: Mass-Energy and Nuclear Binding Energy

Empirically, the radius of a nucleus scales with mass number as $R=R_0{A}^{1/3}$, where $R_0$ is a universal constant.

Nuclear volume then scales as $V=\frac{4}{3}\pi R^3=\frac{4}{3}\pi R_0^{3}A$, which is proportional to $A$.

Nuclear mass is proportional to $A$ (each nucleon has roughly the same mass), so density $\rho =M/V$ has the $A$ dependence cancel.

Nuclear mass density is therefore essentially constant across all nuclei and independent of $A$, matching option (4).