Three concentric metallic spherical shells of radii R, 2R, 3R are given charges Q₁, Q₂, Q₃ respectively, it is found that the surface charge densities on the outer surfaces of the shells are equal. Then the ratio of the charges given to the shells Q₁: Q₂: Q₃ is

The charge distribution on the shells outer surfaces will be:

For shell 1 $\to$Q₁; 

For shell 2 $\to$Q₁ + Q₂;

For shell 3 $\to$Q₁ +  Q₂ + Q₃;

Given that surface charge densities on outer Surfaces of shells are equal. Thus we have

$\mathrm{\sigma }=\frac{{\mathrm{Q}}_1}{4{\mathrm{\pi R}}^2}=\frac{{\mathrm{Q}}_1+{\mathrm{Q}}_2}{4\mathrm{\pi }(2\mathrm{R}{)}^2}=\frac{{\mathrm{Q}}_1+{\mathrm{Q}}_2+{\mathrm{Q}}_3}{4\mathrm{\pi }(3\mathrm{R}{)}^2}$

On solving, we get: Q₁ :Q₂ :Q₃ = 1:3:5.