JEE Main 2022 · 27 Jul · Shift 1 · Physics Q40

← JEE Main 2022 · 27 Jul · Shift 1

PhysicsSingle correct+4 / -1Question 40 of 90

Two identical positive charges Q each are fixed at a distance of '2a' apart from each other. Another point charge $q_0$ with mass 'm' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_0$ executes SHM. The time period of oscillation of charge $q_0$ will be :

\sqrt{\dfrac{4\pi^3\varepsilon_0ma^3}{q_0Q}}

\sqrt{\dfrac{q_0Q}{4\pi^3\varepsilon_0ma^3}}

\sqrt{\dfrac{2\pi^2\varepsilon_0ma^3}{q_0Q}}

\sqrt{\dfrac{8\pi^3\varepsilon_0ma^3}{q_0Q}}

Answer and worked solution

Official answer: A

Restoring force for a small x: $\frac{Qq_0}{4\pi\varepsilon_0}\left[\frac1{(a-x)^2}-\frac1{(a+x)^2}\right]\approx\frac{Qq_0x}{\pi\varepsilon_0a^3}$ .

Period $T=2\pi\sqrt{\frac{\pi\varepsilon_0ma^3}{Qq_0}}=\sqrt{\frac{4\pi^3\varepsilon_0ma^3}{q_0Q}}$ .

(A)

Topics:Simple harmonic motion Coulomb's law and superposition

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JEE Main 2022 · 27 Jul · Shift 1, Physics question 40