Let us consider two homogeneous shells of radii \( r_1 \) & \( r_2 \) respectively and the surface of the material is \( \sigma \).

Now the potentials are,

\( V_1=-G\ \frac{4\pi{r_1}^2\sigma}{r_1}=-G4\pi{r_1}\sigma \)

\( V_2=-G\ \frac{4\pi{r_2}^2\sigma}{r_2}=-G4\pi{r_2}\sigma \)

where \( G \) is the gravitational constant.

therefore, \( {V_1} : {V_2} = {r_1} : {r_2} \),

Now given, \( {V_1} : {V_2} = 3:4 \)

So, \( {r_1} : {r_2} =3:4 \).