The radii of the inner and outer spheres of a spherical capacitor are $9\,cm$ and $10\,cm$ respectively. If the dielectric constant of the medium between the two spheres is $6$ and the charge on the inner sphere is $18 \times 10^{-9}\,C$,calculate the potential of the inner sphere,given that the outer sphere is earthed.

The capacitance of an isolated sphere of radius $r_1$ is increased by $5$ times,when it is enclosed by an earthed concentric sphere of radius $r_2$. The ratio of their radii is

$A$ conductor is connected to a battery of $5\, V$. It acquires a charge of $50\ \mu C$. Calculate the capacitance of the conductor in $\mu F$.

Given below are two statements: One is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A:$ Two metallic spheres are charged to the same potential. One of them is hollow and another is solid,and both have the same radii. The solid sphere will have a lower charge than the hollow one.
Reason $R:$ Capacitance of metallic spheres depends on the radii of the spheres.
In the light of the above statements,choose the correct answer from the options given below.

$64$ small drops of water having same charge and same radius are combined to form one big drop. The ratio of capacitance of the big drop to the small drop is . . . . . . .

$A$ spherical capacitor consists of two concentric spherical conductors,held in position by suitable insulating supports. Show that the capacitance of a spherical capacitor is given by $C = \frac{4 \pi \varepsilon_{0} r_{1} r_{2}}{r_{1} - r_{2}}$,where $r_{1}$ and $r_{2}$ are the radii of outer and inner spheres,respectively.