Consider a spherical drop of mercury of radius $R$ with capacitance $C = 4 \pi \epsilon_0 R$. If two such droplets combine to form a larger one,what would be its capacitance in terms of $C$?

$A$ sphere of $4\, cm$ radius is suspended within a hollow sphere of $6\, cm$ radius. The inner sphere is charged to a potential of $3\, e.s.u.$ and the outer sphere is earthed. The charge on the inner sphere is.....$e.s.u.$

$A$ 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 $6.4 \times 10^6 \, m$.

The dimension of capacitance is:

The unit of permittivity of free space is