The weight of each of two small metal spheres having same amount of charge is 3g. The two spheres are suspended with tow threads of length 13 cm each from a point. Due to mutual repulsion they are at rest at a distance of 10 cm. Determine the charge on each sphere and tension in the threads.

Explanation

Let the two spheres at rest be at A and B
Here `AB=10` cm. The length of each thread `=OA=OB=13cm, theta=` angle made by each thread with the vertical
`T=` tension in each thread and `q=` charge on each sphere.
In equilibrium three forces act on each ball. THese are 1. weight of the ball `=mg` 2. tension in thread `=T` and 3. mutual force of electrostatic repulsion `=F`


In equilibrium of any sphere the vertica component `Tcos theta` of the tension, balances the weight mg of the spehre
`:.T cos theta=mg` or `Txx12/13=3xx980`
`[ :' sin theta=5/12, cos theta=sqrt(1-25/169)=12/13]`
or `T=(3xx980xx134)/12=3185`dyn
Again the repiulsive force F is balanced by the horizontal component `Tsin theta` of tension inthe thread.
`:.F=T sin theta` or `(qxxq)/((10)^(2))=3185xx5/13`
or `q^(2)=245xx500` or `q=350`esu