Question

A pitch ball covered with a tin foil having a mass $m$$kg$ hangs by a fine silk thread of length $l$ metre in an electric field $E$. When the ball is given an electric charge of $q$ coulomb, it stands out $d$ metre apart from the vertical line. The magnitude of the electric force will be:

• A. $\frac{mgd}{\sqrt{l^2-d^2}}$
• B. $\frac{mgd}{al}$
• C. $\frac{mgl}{q\sqrt{l^2-d^2}}$
• D. $\frac{mg{l}^2}{q\left(\sqrt{l^2-d^2}\right)}$

Answer 1

Answer: (A)

$\frac{mgd}{\sqrt{l^2-d^2}}$

Suppose that the thread makes angle $\theta$ with the vertical.

Thus $tan\theta =\frac{d}{\sqrt{l^2-d^2}}$

Since forces perpendicular to the direction of thread must balance each other for the system to be in equilibrium,

$mgsin\theta =Fcos\theta$

$⟹F=mgtan\theta$

$=mg\frac{d}{\sqrt{l^2-d^2}}$

$=\frac{mgd}{\sqrt{l^2-d^2}}$