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प्रश्न
Two identical pith balls, each carrying a charge q, are suspended from a common point by two strings of equal length l. Find the mass of each ball if the angle between the strings is 2θ in equilibrium.
उत्तर
Let the tension in the string be T and force of attraction between the two balls be F.
From the free-body diagram of the ball, we get
Tcos θ = mg ...(1)
Tsin θ = F ...(2)
\[\Rightarrow \tan\theta = \frac{F}{mg}\]
\[ \Rightarrow m = \frac{F}{g\tan\theta} \ldots\left( 3 \right)\]
Here, separation between the two charges,
\[r = 2l\sin\theta\]
\[F = \frac{1}{4\pi \epsilon_0}\frac{q^2}{r^2} = \frac{1}{4\pi \epsilon_0} \times \frac{q^2}{\left( 2l\sin\theta \right)^2}\]
Substituting the value of F in equation (3), we get
\[m = \frac{q^2 \cot\theta}{16\pi \epsilon_0 g l^2 \sin^2 \theta}\]
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