JEE Main 2021 — Physics Waves & Oscillations

2021mcqhard

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?

Official previous-year question

Held on 27 Jul 2021 · Verified 6 Jul 2026.

Options

A
$x={(\frac{{q}^{2}l}{2\pi {\epsilon }_{0}mg})}^{\frac{1}{2}}$
B
$x={(\frac{{q}^{2}l}{2\pi {\epsilon }_{0}mg})}^{\frac{1}{3}}$
C
$x={(\frac{{q}^{2}{l}^{2}}{2\pi {\epsilon }_{0}{m}^{2}g})}^{\frac{1}{3}}$
D
$x={(\frac{{q}^{2}{l}^{2}}{2{\pi \epsilon }_{0}{m}^{2}{g}^{2}})}^{\frac{1}{3}}$

Did you get this right?

Solution

JEE Main 2021 Physics, Oscillations — solution figure

$T\mathrm{cos}\theta =mg$

$T\mathrm{sin}\theta =\frac{k{q}^{2}}{{x}^{2}}$

$\mathrm{tan}\theta =\frac{k{q}^{2}}{{x}^{2}mg}$

as $\mathrm{tan}\theta \approx \mathrm{sin}\theta \approx \frac{x}{2L}$

$\frac{x}{2L}=\frac{K{q}^{2}}{{x}^{2}mg}$

$x={(\frac{{q}^{2}L}{2\pi {\epsilon }_{0}mg})}^{\frac{1}{3}}$

Your note

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Options

$x={(\frac{{q}^{2}l}{2\pi {\epsilon }_{0}mg})}^{\frac{1}{2}}$

$x={(\frac{{q}^{2}l}{2\pi {\epsilon }_{0}mg})}^{\frac{1}{3}}$

$x={(\frac{{q}^{2}{l}^{2}}{2\pi {\epsilon }_{0}{m}^{2}g})}^{\frac{1}{3}}$

$x={(\frac{{q}^{2}{l}^{2}}{2{\pi \epsilon }_{0}{m}^{2}{g}^{2}})}^{\frac{1}{3}}$

Solution

JEE Main 2021 Physics, Oscillations — solution figure

$T\mathrm{cos}\theta =mg$

$T\mathrm{sin}\theta =\frac{k{q}^{2}}{{x}^{2}}$

$\mathrm{tan}\theta =\frac{k{q}^{2}}{{x}^{2}mg}$

as $\mathrm{tan}\theta \approx \mathrm{sin}\theta \approx \frac{x}{2L}$

$\frac{x}{2L}=\frac{K{q}^{2}}{{x}^{2}mg}$

$x={(\frac{{q}^{2}L}{2\pi {\epsilon }_{0}mg})}^{\frac{1}{3}}$

JEE Main 2021 — Physics Waves & Oscillations

Options

Did you get this right?

Solution

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JEE Main Waves & Oscillations in other years

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JEE Main 2021 — Physics Waves & Oscillations

Options

Did you get this right?

Solution

Your note

JEE Main Waves & Oscillations in other years

More JEE Main Waves & Oscillations questions

Other Physics topics for JEE Main

Mechanics

Electromagnetism

Modern Physics

Optics

Thermodynamics

Keep practicing Waves & Oscillations