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

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

If the circumference of a sphere is $3 \ m$,then the capacitance of the sphere in water is (dielectric constant of water = $80$) (in $pF$)

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 $C$?

The potentials of the two plates of a capacitor are $+10\,V$ and $-10\,V$. The charge on one of the plates is $40\,C$. The capacitance of the capacitor is........$F$.

The capacitance $(C)$ of an isolated conducting sphere of radius $(a)$ is given by $4\pi \varepsilon_0 a$. If this sphere is enclosed by an earthed concentric sphere of radius $(b)$,and the ratio of the radii of the spheres is $\frac{b}{a} = n$,then the capacitance of such a system will be increased by a factor of: