Plzzzzzzzzzzzzzzoooooooooooooooooooolkoolook solve question number 7

To find Potential due to a non conducting sphere
total charge inside it be ‘Q’
volumetric charge density be ‘ρ’.
Let R be the radius of the sphere.
We need to calculate potential due to a conducting shell at distance r such that it is inside sphere

We know the relation between volumetric charge density (ρ) and total charge within the volume (Q) :

We also know,

We also know the relation between electric field (E) and potential (dV)
Let the distance r from centre  enclose a small sphere with radius r and charge q.

                         Q/R³ = q/r³     (from eq 1)

Integrating above equation and applying limits from r to R

kQR²/R³ - Vr = kQr²/2R³ - kQR²/2R³
Vr = 3kQR²/2R³ - kQr²/2R³

        =kQ/2R³ (3R² - r²)

Ans is (A)