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=` constant `= (q)/(A)rArrq alpha A rarr`
Ratio of charges `q_(1):q_(2)=1:4`.
`:. (1) rArr (q_(1))/(q_(2))=(A_(1))/(A_(2))=(1)/(4)`
`(4 pi r_(1)^(2))/(4 pi 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.