With increase in the number of electrons in the same shell, the atomic radii decreases due to increase in effective nuclear charge. However, atomic radii increases, as the number of shells increases. Thus, on moving down a group atomic radii increases.
The electronic configuration of the given elements is
$\begin{aligned}
\mathrm{Mg}_{12} & =[\mathrm{Ne}] 3 \mathrm{~s}^2 \\
\mathrm{Ca}_{20} & =[\mathrm{Ar}] 4 \mathrm{~s}^2
\end{aligned}$
$\begin{array}{r}
\mathrm{P}_{15}=[\mathrm{Ne}] 3 \mathrm{~s}^2 3 \mathrm{p}^3 \\
\mathrm{Cl}_{17}=[\mathrm{Ne}] 3 \mathrm{~s}^2 3 \mathrm{p}^5
\end{array}$
In $\mathrm{Mg}, \mathrm{P}$ and $\mathrm{Cl}$, the number of electrons are increasing in the same shell, thus the order of their atomic radii is
$\mathrm{Cl} < \mathrm{P} < \mathrm{Mg}$
In $\mathrm{Ca}$, the electron is entering in higher shell, thus, it has the highest atomic radii among the given. Thus, the order of radii is
$\mathrm{Cl} < \mathrm{P} < \mathrm{Mg} < \mathrm{Ca}$