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Q.

Two similar metal spheres are suspended by silk threads from the same point. When the spheres are given equal charges of 2 $μ$ C the distance between them becomes 6cm. If length of each thread is 5 cm, the mass
of each sphere is (g=10 m/s²)

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a

$\frac{4}{3} kg$

b

4 kg

c

$\frac{1}{3} kg$

d

3 kg

answer is C.

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Detailed Solution

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$\begin{array}{l} F = mgTan θ \\ \frac{1}{4 {πε}_{0}} \frac{q_{1} q_{2}}{r^{2}} = mg \frac{3}{4} \\ 9 \times 10^{9} \times \frac{2 \times 10^{- 6} \times 2 \times 10^{- 6}}{{(6 \times 10^{- 2})}^{2}} \\ = m \times 10 \times \frac{3}{4} \\ 10 = m \times 10 \times \frac{3}{4} \Rightarrow m = \frac{4}{3} kg \end{array}$

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Two similar metal spheres are suspended by silk threads from the same point. When the spheres are given equal charges of 2μC the distance between them becomes 6cm. If length of each thread is 5 cm, the massof each sphere is (g=10 m/s2)