A small block `A` of mass `m=5kg` and charge `2xx10^(-7)C` is kept on a fixed non conducting inclined plane whose inclination is `theta=tan^(-1)(3//4)`. The coefficient of friction between block `A` and inclined plane is `mu=0.5`. Another charged small block `B` is fixed at the bottom of the inclined plane. The distance between `A` and `B` is `l=3cm`. If `Q_(1)` and `Q_(2)` are the magnitudes of the minimum and maximum values of charges of `B` for which the block `A` does not slide then find the value of `(Q_(2))/(Q_(1))`.
(Take `g=10m//s^(2)`)

Answer

5

Explanation

`mgsintheta=5xx10xx3/5=30N`
`mumgcostheta=0.5xx5xx10xx4/5=20N`
as `mgsinthetagtmucostheta`
so charges must be of same sign
Nor for maximum `Q`
`implies(kq_(0)Q_(max))/(r^(2))=mgsintheta+f_(smax)=50N`
`Q_(max)=50/2xx10^(-6)=25xx16^(-6)`
similarly `Q_(min)=(kqQ_(min))/(r^(2))=mgsintheta-f_(s)max`
`Q_(min)5xx10^(-6)C`
`(Q_(max))/(Q_(min))=25/5=5`