A spherical conductor placed in vacuum has capacitance of $3.14×10^{-9} F$. Its radius will be

28.3 m

The correct answer is Option (1) → 28.3 m

Given:

Capacitance, $C = 3.14 \times 10^{-9}\ \text{F}$

For a spherical conductor in vacuum:

$C = 4 \pi \epsilon_0 R$

Solving for $R$:

$R = \frac{C}{4 \pi \epsilon_0}$

Substitute values ($\epsilon_0 = 8.85 \times 10^{-12}\ \text{F/m}$):

$R = \frac{3.14 \times 10^{-9}}{4 \pi \cdot 8.85 \times 10^{-12}}$

$R = \frac{3.14 \times 10^{-9}}{111.1 \times 10^{-12}} \approx 28.25\ \text{m}$

∴ Radius of the spherical conductor = 28.25 m