Question

A charged cork ball of mass 1 g is suspended on a light string in the presence of a uniform electric field as shown. When $\overrightarrow{E}=(3\hat{i}+5\hat{j})\times {10}^{5}N{C}^{-1}$, the ball is in equilibrium at $\theta =37$. T is the tension in the string and q is the charge on the ball (Take sin 37 = 0.60 and $g=10m{s}^{-2}$)

• A. Q = 21 nC
• B. q = 12 nC
• C. $T=5.55\times {10}^{-3}N$
• D. $T=4.55\times {10}^{-3}N$

Answer 1

The correct option is C $T=5.55\times {10}^{-3}N$

$T=cos\theta +q{E}_y=mg$ ...........(1)
$T=sin\theta =q{E}_x$
$\Rightarrow T\left(0.6\right)=3\times {10}^{5}q$
$\Rightarrow q=\frac{60}{3}\times {10}^{-5}T$
$\Rightarrow q=2\times {10}^{-6}T$
$\Rightarrow T\left(0.8\right)+T=\frac{10}{100}$
$\Rightarrow T=5.55\times {10}^{-3}N$
$\Rightarrow q=11.1\times {10}^{-9}C$
$\Rightarrow q=11nC$