Three identical small balls, each of mass 0.1 g, are suspended at one point on silk thread having a length of `l = 20cm` . What charges should be imparted to the balls for each thread to form an angle of `alpha = 30^@` with the vertical?

Answer

A, C

Explanation

F= Electrostastic force between two charged balls.
`sqrt3F=`Resultant of electrostatic force on any one balll from rest two balls.

`a=lcos60^@=10cm`
`r=2acos30^@`
`(2)(10)(sqrt3/2)=10sqrt3cm`
Now applying Lami's theorem for the equilibrium of ball we have
`(mg)/(sin(90^@+30^@))=(sqrt3F)/(sin(90^@+60^@))`
`F=(mg)/3=1/(4piepsilon_0)((q)(q))/r^2=(mg)/3`
`:. q=sqrt((mgr^2)/(3(1//4piepsilon_0))`
`=sqrt(((0.1xx10^-3)(9.8)(10sqrt3xx10^-2)^2)/(3xx9xx10^9))`
`=3.3xx10^-8C`