Liquid $A$ rises to a height of $10 \ cm$ in a capillary tube and liquid $B$ falls to a depth of $2 \ cm$ in the same tube. The densities of $A$ and $B$ are $1 \ g/cm^3$ and $10 \ g/cm^3$ respectively. The contact angles of $A$ and $B$ with the tube are $0^{\circ}$ and $135^{\circ}$ respectively. If the surface tensions of $A$ and $B$ are $S_A$ and $S_B$, then the ratio $\frac{S_B}{S_A}$ is:

• A
  $\sqrt{2}$
• B
  $2 \sqrt{2}$
• C
  $\frac{1}{\sqrt{2}}$
• D
  $\frac{1}{2 \sqrt{2}}$