A charged cork ball of mass m is suspended on a light string in the presence of a uniform electric field as shown in fig. When `E=(A hat i+B hat j)NC^(-1)`, Where A and B positive numbers, the ball is in equilibrium at `theta`. Find (a) the charge on the ball and (b) the tension in the string.

Options

A. `q= (mg)/(A+B tan theta)`
B. `q = (mg tan theta)/(A+B)`
C. `q = (mg tan theta)/(A+B tan theta)`
D. `q=(Amg)/(A+B)`

Answer

C

Explanation

`qA = T sin theta` .........(2)
`qB + T cos theta = mg` ........(2)
`qB + (qA cos theta)/(sin theta) = mg`
`q [B +(A)/(tan theta)] = mg`
`q = (mg tan theta)/(A +B tan theta)`