1. Use the nuclear radius formula

   For a nucleus of mass number $A$, the radius is $R = R_0 A^{1/3}$ where $R_0$ is a constant.

2. Write the expression for nuclear density

   Nuclear density is $\rho = \frac{\text{mass of nucleus}}{\text{volume of nucleus}}$

   The nuclear mass is approximately proportional to $A$: $m \propto A$

   The nuclear volume is $V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi (R_0 A^{1/3})^3$ $V = \frac{4}{3}\pi R_0^3 A$

   Hence, $\rho \propto \frac{A}{A} = \text{constant}$

3. Compare densities of $^{40}\text{Ca}$ and $^{16}\text{O}$

   Since nuclear density is approximately independent of $A$, $\frac{\rho_{\mathrm{Ca}}}{\rho_{\mathrm{O}}} \approx 1$

4. Check options

   • A: $1$ ✅
   • B: $5$ ❌
   • C: $0.1$ ❌
   • D: $2$ ❌

Therefore, the correct option is A.