c
We know resonant frequency \(\mathrm{f}=\frac{1}{2 \pi \sqrt{\mathrm{LC}}}\dots (1)\)

and when the chamber is filled by a gas then resonant frequency is given by;

\(\mathrm{f}-\mathrm{f}_{0}=\frac{1}{2 \pi \sqrt{\mathrm{LC}_{0}}}\dots(2)\)

Dividing eqn \((1)\) by eqn \((2)\)

\(\frac{\mathrm{f}}{\mathrm{f}-\mathrm{f}_{0}}=\sqrt{\frac{\mathrm{C}_{\mathrm{g}}}{\mathrm{C}_{0}}}\)

\(\frac{10000}{10000-50}=\sqrt{\mathrm{k}}\)

\(\mathrm{k}=1.01\)