A charge $Q$ is distributed over three concentric spherical shell of radii $a, b, c (a < b < c)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre, where $r < a$, would be
JEE MAIN 2019, Diffcult
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$\mathrm{Q}_{1}+\mathrm{q}_{2}+\mathrm{Q}_{3}=\mathrm{Q}.........(1)$
$\frac{\mathrm{Q}_{1}}{4 \pi \mathrm{a}^{2}}=\frac{\mathrm{Q}_{2}}{4 \pi \mathrm{b}^{2}}=\frac{\mathrm{Q}_{3}}{4 \pi \mathrm{c}^{2}}=\mathrm{k}.........(2)$
Subs. $Q_{1}, Q_{2}, Q_{3}$ in $( 1)$
$k=\frac{Q}{4 \pi\left(a^{2}+b^{2}+c^{2}\right)}$
$v=\frac{k Q_{1}}{a}+\frac{k Q_{2}}{b}+\frac{k Q_{3}}{c}$
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