Three concentric conducting spherical shells have radii r, 2r, and 3r and charges `q_1,q_2 and q_3`, respectively. Innermost and outermost shells are earthed as shown in figure. The charges shown are after earthing. Select the correct alternative.

Options

A. `Q_(1)+Q_(3)=-Q_(2)`
B. `Q_(1)=(-Q_(2))/4`
C. `Q_(3)/Q_(1)=3`
D. `Q_(3)/Q_(2)=(-1)/3`

Answer

D

Explanation

Potential at outermost shell
`=(KQ_(1))/(3r)+(KQ_(2))/(3r)+(KQ_(3))/(3r)=0`
`rArr Q_(1)+Q_(2)+Q_(3)=0` …(i)
and potential at innermost surface
`(KQ_(1))/(r)+(KQ_(2))/(2r)+(KQ_(3))/(3r)=0`
`rArr (K[6Q_(1)+3Q_(2)+2Q_(3)])/(6r)=0` ...(ii)
From eq. (i) & (ii) `Q_(1)=-Q_(2)/4` and also `Q_(2)/Q_(1)=3`