Three concentric metallic spherical shells of radii R, 2R, 3R are given charges `Q_(1) Q_(2) Q_(3)`, respectively. It is found that the surface charge densities on the outer surface of the shells are equal. Then, the ratio of the charges given to the shells `Q_(1) : Q_(2) : Q_(3)` is

Options

A. `1:2:3`
B. `1:3:5`
C. `1:4:9`
D. `1:8:18`

Answer

B

Explanation

`Q_(1)=sigma4pi R^(2)=k` (say)
`Q_(1)+Q_(2)=sigma4pi(4R^(2))=4k`
`Q_(1)+Q_(2)+Q_(3)=sigma(4pi)(9r^(2))=9k`
On solving, `Q_(1):Q_(2):Q_(3) : : 1:3:5`