a
Capacitance of isolated Conducting sphere \(=4 \pi \varepsilon_{0} R_{1}\)

By enclosing inside another sphere of radius \(R_{2}\), new capacitance \(=\frac{4 \pi \varepsilon_{0} R_{1} R_{2}}{\left(R_{2}-R_{1}\right)}\)

Given: \(\frac{4 \pi \varepsilon_{0} R_{1} R_{2}}{\left(R_{2}-R_{1}\right)}=n \times 4 \pi \varepsilon_{0} R_{1}\)

\(\frac{ R _{2}}{\left( R _{2}- R _{1}\right)}= n \Rightarrow \frac{\frac{ R _{2}}{ R _{1}}}{\left(\frac{ R _{2}}{ R _{1}}-1\right)}= n\)

\(\frac{ R _{2}}{ R _{1}}= n \frac{ R _{2}}{ R _{1}}- n \Rightarrow \frac{ R _{2}}{ R _{1}}=\frac{ n }{( n -1)}\)