Eight drops of mercury of equal radii combine to form a big drop. The capacitance of a bigger drop as compared to each smaller drop is (in $times$)

If the energy stored in a spherical conductor having a charge of $12 \mu C$ is $6 \ J$,then the radius of the spherical conductor is (in $cm$)

The stratosphere acts as a conducting layer for the Earth. If the stratosphere extends up to $50 \ km$ from the Earth's surface,calculate the capacitance of the spherical capacitor formed between the Earth's surface and the stratosphere in $F$. Take the radius of the Earth as $6400 \ km$.

$A$ spherical capacitor has an inner sphere of radius $12 \;cm$ and an outer sphere of radius $13 \;cm$. The outer sphere is earthed and the inner sphere is given a charge of $2.5 \;\mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant $32$.
$(a)$ Determine the capacitance of the capacitor.
$(b)$ What is the potential of the inner sphere?
$(c)$ Compare the capacitance of this capacitor with that of an isolated sphere of radius $12 \;cm$. Explain why the latter is much smaller.

This question has Statement $1$ and Statement $2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement $1$ : It is not possible to make a sphere of capacity $1 \, F$ using a conducting material.
Statement $2$ : It is possible for Earth as its radius is $6.4 \times 10^6 \, m$.

What is the capacitance of a spherical conductor with a radius of $1 \ m$?