Two identical tennis balls each having mass m and charge q are...

Two identical tennis balls each having mass

m

and charge

q

are suspended from a fixed point by threads of length

l .

What is the equilibrium separation when each thread makes a small angle

\theta

with the vertical? Two identical tennis balls each having mass m and charge q are suspended from a fixed point by threads of length l .

Options

Ax = $\left(\dfrac{{q}^{2}l}{2\pi{ε}_{0}mg}\right)\dfrac{1}{2}$
Bx = $\left(\dfrac{{q}^{2}l}{2\pi{ε}_{0}mg}\right)\dfrac{1}{3}$
Cx = $\left(\dfrac{{q}^{2}{l}^{2}}{2\pi{ε}_{0}{m}^{2}g}\right)\dfrac{1}{3}$
Dx = $\left(\dfrac{{q}^{2}{l}^{2}}{2{\pi ε}_{0}{m}^{2}{g}^{2}}\right)\dfrac{1}{3}$

Correct answer

B. x = $\left(\dfrac{{q}^{2}l}{2\pi{ε}_{0}mg}\right)\dfrac{1}{3}$

Step-by-step solution

Two identical tennis balls each having mass m and charge q are suspended from a fixed point by threads of length l .

Tcos\theta = mg $<br />Tsin\theta = \dfrac{k{q}^{2}}{{x}^{2}}$
$tan\theta = \dfrac{k{q}^{2}}{{x}^{2}mg}$
as $tan\theta \approx sin\theta \approx \dfrac{x}{2L}$
$\dfrac{x}{2L} = \dfrac{K{q}^{2}}{{x}^{2}mg}$
$x = \left(\dfrac{{q}^{2}L}{2\pi{ε}_{0}mg}\right)\dfrac{1}{3}$

Practice Oscillations on Quantrex Academy →

More from Oscillations

A tank contains two immiscible liquids of densities 6ρ and 2ρ . The higher density liquid… JEE Advanced 2026 The frequency of oscillation of a mass m suspended by a spring is v_1 . If the length of… JEE Main 2026 A spring stretches by 2 mm when it is loaded with a mass of 200 g. From equilibrium… JEE Main 2026 A particle is executing simple harmonic motion. Its amplitude is A and time period is 5… JEE Main 2026 Match List-I with List-II. List-I List-II A. ^2 ω t I. Periodic with time period T =… JEE Main 2026 A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in… JEE Main 2026 The velocity of a particle executing simple harmonic motion along x -axis is described as… JEE Main 2026 The equation of motion of a particle is given by x = a (50t + (π)/(3)) cm. The particle… JEE Main 2026 Full Oscillations list All JEE Main PYQs