Q.Which of the following properties of a nucleus does not depend on its mass number? (A) radius (B) mass (C) volume (D) density

[!TLDR] Radius ($\propto A^{1/3}$), mass ($\propto A$) and volume ($\propto A$) all depend on mass number A, but density works out to a …

Check each property against the standard nuclear-size relations. Radius: $R=R_0A^{1/3}$ -- explicitly depends on A. Mass: the nuclear mass is approximately $M\approx mA$ (m being the average nucleon mass) -- explicitly proportional to A. Volume: since $V=\frac{4}{3}\pi R^3=\frac{4}{3}\pi R_0^3A$ -- also explicitly proportional to A. Density: $\rho=M/V=\frac{mA}{\frac{4}{3}\pi R_0^3A}=\frac{3m}{4\pi R_0^3}$ -- here the A in the numerator and denominator CANCEL exactly, leaving a …

Substitute $R=R_0A^{1/3}$ into the definitions of mass, volume and density in turn, and check w …

Assuming a larger nucleus (bigger A) must automatically be 'denser' since it has more mass, without realising the volume grows in exact …