Two spheres of equal charge densities have charges in the ratio 1 : 4 on their surfaces Then the ratio of their volumes

Explanation

Let the charge densities of two spheres be ` sigma_1 = sigma_2 = sigma=(q)/(A)`. For given two sphere , the charge density is the same.
`:. sigma ` = constant `=(q)/(A) implies q prop A to`
Ratio of charges `q_1 : q_2 = 1:4`
`:. (1) implies (q_1)/(q_2) = (A_1)/(A_2) = (1)/(4)`
`(4 pi r_1^(2))/( 4pi r_2^(2)) = (1)/(4)`
` (r_1)/(r_2) = sqrt((1)/(4)) = (1)/(2)`
`:.` Ratio of their volumes `=(v_1)/(v_2)=((4//3) pi r_1^(3))/((4//3)pi r_2^(3))`
`(v_1)/(v_2) = ((r_1)/(r_2))^(3) = ((1)/(2))^(3)`
`v_1 : v_2 =1 :8`
`:.` Ratio of their volumes = 1:8