A 5 g weight is fastened to two helium-filled balloons with the help of a 1m long thread. Both the balloons carry the same charge q and the distance between them in 0.6 m when the system hangs in equilibrium. The charge q is

Options

A. `0.56 muC`
B. `1 muC`
C. `5.6muC`
D. `1 nC`

Answer

A

Explanation

See the figure for the force diagram of a complete system and also the separate force diagram for single balloon.

Here B is buoyant force and other symbols are obvious. For vertical equilibrium of the complete system we can write: 2B = mg `rArr` B = mg/2
=(0.5) `(5xx10^(-3))` (9.8)
Now we can write equations for the force diagram of a single balloon.
Vertical equilibrium of balloon: B = T cos `theta`
Horizontal equilibrium of ballorn: T sin `theta = F_"el"`
Hence we have the following equation
`(sin theta)/(cos theta)=F_"el"/B` ...(i)
`F_"el"=1/(4piepsilon_0)q^2/(0.6)^2`