Answer:
Option C
Explanation:
When metal plate of thickness 2mm is inserted into a parallel plate capacitor , then the arrangement is shown as,
Given , thickness of plate, t=2mm and area, A=$36 \pi cm^{2}$
The above circuit can be redrawn as,
where, $C_{1}=\frac{\epsilon_{0}A}{d_{1}}$ and $C_{2}=\frac{\epsilon_{0}A}{d_{2}}$
Now, $ C_{eq}= \frac{C_{1}C_{2}}{C_{1}+C_{2}}$ (In the series combination)
$\Rightarrow C_{eq}=\epsilon_{0}A\left[\frac{\frac{1}{d_{1}}\times\frac{1}{d_{2}}}{\frac{1}{d_{1}}+\frac{1}{d_{2}}}\right]=\frac{\epsilon_{0}A}{d_{1}+d_{2}}$
$\Rightarrow C_{eq}=\frac{1}{4 \pi \times 9 \times 10^{9}}\times\frac{36 \pi \times 10^{-4}}{3\times 10^{-3}+1\times 10^{-3}}$
$\left( \because \frac{1}{4 \pi\epsilon_{0}}={ 9 \times 10^{9} Nm^{2}/C^{2}}\right)$
=$\frac{1}{4} \times 10^{-10}$=$25 \times 10^{-12}$ F=25pF
so, the correct option is (c)