The insulation property of air breaks down at E= 3 x 10⁶ V /m. The maximum charge that can be given to a sphere of diameter 5m is approximately (in coulombs)

$$\begin{gathered} \mathrm{E}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\times \frac{\mathrm{q}}{{\mathrm{r}}^2}=9\times {10}^9\times \frac{\mathrm{q}}{{\mathrm{r}}^2} \\ \therefore \mathrm{q}=\frac{\mathrm{E}\times {\mathrm{r}}^2}{9\times {10}^9}=\frac{3\times {10}^6\times (2.5{)}^2}{9\times {10}^9}=2.0833\times {10}^{-3} \end{gathered}$$

q should be less than 2.0833 x 10^-3. In the given set of options 2 x 10^-3 is the maximum charge which is smaller than 2.0833 x 10^-3.