Two similar balloons filled with helium gas are tied to `L m` long string. A body of mass `m` is tied to another ends of the strings. The balloons float on air at distance `r`. If the amount of charge on the ballons is same then the magnitude of charge on each balloon will be

Options

A. `[(mgr^(2))/(2k)tan theta]^(1//2)`
B. `[(2k)/(mgr^(2))tan theta]^(1//2)`
C. `[(mgr)/(2k)cot theta]^(1//2)`
D. `[(2k)/(mgr)tan theta]^(1//2)`

Answer

a

Explanation

In equlibrium
`2R= mg` ….(i)
`F_(e )= t sin theta`….(ii)
`R= T cos theta` ….(iii)
From equation (i) and (iii)

`2T cos theta= mg`
Dividing equation (ii) by equation (iv)
`1/2 tan theta= (F_(e))/(mg)`
`implies 1/2 tan theta=(k(Q^(2))/(r^(2)))/(mg)implies theta= ((mgr^(2))/(2k)tan theta)^(1//2)`