The following diagram shows three metal balls Ball `A` is charged to `Q` coulombs and `B,C` are unchanged .The charges on balls `B,C` when the switches `S_(1)` and `S_(2)` are closed are respectively

Options

A. `(8Q)/(23),(3Q)/(23)`
B. `(3Q)/(23),(8Q)/(23),`
C. `(-8Q)/(23),(-3Q)/(23)`
D. `(-3Q)/(23),(-8Q)/(23)`

Answer

C

Explanation

Let charge on `B` and `C` are respectively `q_(1)` and `q_(2)`
`V_(B)=0`
`rArr (1)/(4piepsilon_(0))(Q)/(5a)+(1)/(4piepsilon_(0))(q_(1))/(2a)+(1)/(4piepsilon_(0))(q_(2))/(5a)=0`
`rArr (q_(1))/(2a)+(q_(2))/(5a)+(Q)/(5a)=0....(1)`
`V_(c)=0`
`(1)/(4piepsilon_(0))(Q)/(5a)+(1)/(4piepsilon_(0))(q_(2))/(a)=0`
`(q_(1))/(5a)+(q_(2))/(a)+(Q)/(5a)=0....(2)`
`rArr (q_(1))/(2a)+(q_(2))/(5a)=(q_(1))/(5a)+(q_(2))/(a)(q_(1))/(2)+(q_(2))/(5)=(q_(1))/(5)+q_(2)`
`q_(1)(3)/(10)=q_(2)(4)/(5)3q_(1)=8q_(2)rArr (q_(1))/(2a)+(3q_(1))/(40a)+(Q)/(5a)=0`
`\(q_(1))/(2)+(3q_(1))/(40)=-(Q)/(5)(23q_(1))/(40)=-(Q)/(5)q_(1)=(8Q)/(23)`
` q_(2)=(3q_(1))/(8)=-(3Q)/(23)`