Two small balls, each having equal positive charge `Q` are suspended by two insulation strings of equal length `l` from a hook fixed to a stand. It mass of each ball `=m` and total angle between the two strings is `60^(@)`m, then find the charge on each ball.

Options

A. `sqrt((mg)/(4piepsilon_(0)l^(2)))`
B. `sqrt(2piepsilon_(0)l^(2)mg)`
C. `sqrt((piepsilon_(0)l^(2)mg)/(4)`
D. `sqrt((4piepsilon_(0)l^(2)mg)/(sqrt3)`

Answer

d

Explanation

Force on one ball due to charge of other ball `=QE(Q^(2))/(4piepsilon_(0)(2l//sintheta)^(2))=(kQ^(2))/(4l^(2)sin^(2)theta)`

Since the system is balanced,
`T sin theta=(kQ^(2))/(4l^(2)sin^(2)theta)`
`T cos theta = mg`
`tan theta = (kQ^(2))/(4l^(2)sin^(2)theta.mg)`
`Q=sqrt((4l^(2) sin^(2)theta.tan thetamg)/(k))=sqrt((l^(2))/(ksqrt(3))mg)=sqrt((4piepsilon_(0)l^(2))/(sqrt(3))mg)`