Question

The capacity of an isolated sphere of radius $9cm$ is $C$. When it is connected to an earthed concentric thin hollow sphere of radius $R$, the capacity becomes $10C$. Then the value of $R$ is

• A. $9cm$
• B. $10cm$
• C. $90cm$
• D. $100cm$

Answer 1

The correct option is B $10cm$

$C=4\pi {ϵ}_{0}r10C=4\pi {ϵ}_0\frac{rR}{R-r}\Rightarrow 10=\frac{R}{R-r}\Rightarrow R=\frac{10}{9}r=\frac{10}{9}\times 9=10cm$