The capacitor of an oscillatory circuit of frequency 10,000 Hz is enclosed in a container.When the container is evacuated , the frequency changes by 50 Hz, the dielectric constant of the gas is
Correct option is B. 1.01
$$f=\dfrac{1}{2 \pi \sqrt{LC}} $$
$$,f+50=\dfrac{1}{2 \pi \sqrt{LC / k}}$$
$$\Rightarrow K=(\dfrac{f+50}{f})^2=(1+\dfrac{50}{f})^2$$
$$\Rightarrow K=1+\dfrac{100}{f}$$
$$=1+\dfrac{100}{10000}=1:01$$