There are two concentric and coplanar non-conducting rings of radii `R` and `4R`. The charge is distributed uniormly on both rings. The charge on smaller ring is `q` and charge on large ring is `-8q`. A particle of mass `10g` and charge `-q` is projected along the axis from infinity. What is the minimum speed of charge at infinity to reach the common centre of rings (take `(Kq^(2))/R=(2sqrt(5))/3J`)

Options

A. `5m//s`
B. `10m//s`
C. `20m//s`
D. `30m//s`

Answer

C

Explanation

`vecE_(q)+vecE_(8q)=vec0`
`implies(Kqx)/((R^(2)+x^(2))^(3//2))=(k(8q)x)/((16R^(2)+x^(2))(3//2))`
`impliesx=2R`
In region `xgt2R` electrostatics force is repulsive
in region `0ltxlt2R` electrostatics force is attractive
If change paticle crosses `x=2R` it will reach origin so by conservation of energy
`:. 1/2mv^(2)=-(kqxxq)/(sqrt(R^(2)+x^(2)))+(k(8q)xxq)/(sqrt(16R^(2)+x^(2)))`
`implies v=20m//s`