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 what is the ratio of the charges given to the shells, Q1​:Q2​:Q3​, ?

1:4:9

The correct answer is Option (2) → $1:4:9$

$λ = \frac{Q}{4\pi R^2}$

$⇒λ_1 = \frac{Q_1}{4\pi R^2},λ_2 = \frac{Q_2}{16\pi R^2},λ_3= \frac{Q_3}{36\pi R^2}$

$λ_1 = λ_2 = λ_3$ [Given]

$⇒Q_1=\frac{Q_2}{4}=\frac{Q_3}{9}⇒Q_1:Q_2:Q_3=1:4:9$