Question

Two small conducting spheres each of mass $9 \times 10^{-4}$g are suspended from the same point by non conducting strings of length 100 cm. They are given equal and similar charges until the strings are equally inclined at $45^\circ$ each to the vertical. The charge on each sphere is .......coulomb

• A. $1.4 \times 10^{-6}$
• B. $1.6 \times 10^{-6}$
• C. $2 \times 10^{-6}$
• D. $1.96 \times 10^{-6}$

Answer 1

Answer: (A)

Mass of the sphere $=9 \times 10-4 kg$ (Given)
Length of the string $=100 cm$ (Given)
Angle of inclination $=45^{\circ}$ (Given)
Let $T \cos 45^{\circ}=m g \cdots$ (1)
$= T \sin 45^{\circ}= Kq ^{2} /(2 l \sin 45)^{2} \cdots(2)$
Dividing equation (2) by (1)
$
\begin{array}{l}
=1= Kq ^{2} /(2 l .1 / \sqrt{2})^{2} \\
= q ^{2}=2 l ^{2} \times m \times g / K \\
= q ^{2}=2 \times 9 \times 10^{\prime}-4 \times 10 / 9 \times 10^{\prime} 9 \\
= q ^{2}=2 \times 10^{-12} \\
q =1.414 \times 10^{-6} C
\end{array}
$
Thus, the charge on each sphere is $1.414 \times 10^{-6} C$.