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