A conducting sphere of radius `10 cm` is charged `10 muC`. Another uncharged sphere of radius `20 cm` is allowed to touch it for some tome. After that if the sphere are separted, then surface density of chsrges, on the spheres will be in the ratio of

Options

A. `1:4`
B. `1:3`
C. `2:1`
D. `1:1`

Answer

C

Explanation

Common potential
`V=(Q+0)/(C+2C)=(Q)/(3C)`
final charges
`Q'_(1)=C.(Q)/(3C)=Q//3`
`Q'_(2)=2C.(Q)/(3C)=(2Q)/(3)`
`(sigma'_(1))/(sigma'_(2))=((Q//3)//A)/((2Q//3)//4A)=(2)/(1)`