As the mass number A increases, which of the following quantities related to a nucleus does not change?

Density

The correct answer is Option (3) → Density

The volume of a nucleus increases with mass number $A$ since $V \propto A$.

The mass also increases with $A$, though not linearly due to binding energy considerations.

The binding energy increases with $A$ initially and then saturates or varies slightly depending on nuclear stability.

The nuclear density, however, remains nearly constant for all nuclei. This is because both mass and volume increase proportionally with $A$:

$\text{Density} = \frac{\text{Mass}}{\text{Volume}} \approx \frac{A}{A} = \text{constant}$