Question

A pendulum bob of mass $80mg$ and carrying a charge of $2\times {10}^{-8}coul.$ is at rest in a horizontal uniform electric field of $20,000V{m}^{-1}$. Find the tension in the thread of pendulum:

• A. $8.8\times {10}^{-2}N$
• B. $8.8\times {10}^{-3}N$
• C. $8.8\times {10}^{-4}N$
• D. $8.8\times {10}^{-5}N$

Answer 1

The correct option is C $8.8\times {10}^{-4}N$

Mass $=80mg$

Charge $=2\times {10}^{-8}$ Coulomb

Electric field $=20,000V{m}^{-1}$

Given, mass $=80mg=8\times {10}^{-6}kg$

charge $=q=2\times {10}^{-8}C$

Let $T$ be the tension in string and $\theta$ is the angle if string with vertical.

In equilibrium

$T\sin \theta =qE⟶\left(1\right)$

$T\cos \theta =mg⟶\left(2\right)$

Divide $\left(1\right)$ by $\left(2\right)$ we get

$\tan \theta =\frac{qE}{mg}$

$\Rightarrow \tan \theta =\frac{2\times {10}^{-8}\times 2\times {10}^4}{80\times {10}^{-6}\times 10}$

$\tan \theta =0.5$

$\theta ={\tan }^{-1}\left(0.5\right)$

$\theta ={27}^0$

Now,

tension, $T=\frac{qE}{\sin \theta }=\frac{2\times {10}^{-8}\times 2\times {10}^4}{\sin {27}^0}=8.8\times {10}^{-4}V$