Question

Two charged pendulums of charges $\frac{2}{3} \mu C \,\&$ $\frac{10}{3} \,mC$ are in equilibrium when they are $1\, m$ apart. If the pendulums are identical then what will be the mass of each pendulum if the angle between the strings in equilibrium is $60^{\circ}$

• A. $1 \,Kg$
• B. $2 \,Kg$
• C. $2 \sqrt{3} \,Kg$
• D. $3 \sqrt{2}\, Kg$

Answer 1

Answer: (C)

Force between the charges
$F=\frac{\left(9 \times 10^{9}\right)\left(\frac{2}{3} \times 10^{-6}\right)\left(\frac{10}{3} \times 10^{-3}\right)}{1^{2}}=20\, N$

For equilibrium
$T \sin 30^{\circ}=20$
$T \cos 30^{\circ}= mg$
$\tan 30^{\circ}=\frac{20}{ mg }$
$\Rightarrow m =2 \sqrt{3}\, Kg$