KVPY SX SB Exam 2016 Question Paper

Let at the corner of cube potential = ${\mathit{V}}_0$
Potential
$\mathit{Q}=\mathrm{\rho }\times {\mathit{a}}^3$
So potential $\propto \frac{\mathrm{\rho }{\mathit{a}}^3}{\mathit{a}}$
Potential $\propto {\mathit{a}}^2$Big cube consist of 8 cube
At centre of big cube of side 2a, potential is $8{\mathit{V}}_0$
Potential at corner of big cube $={\mathit{V}}_0\times {\left(2\right)}^2=4{\mathit{V}}_0$
Required ratio $=\frac{8{\mathit{V}}_0}{4{\mathit{V}}_0}=2:1$