JEE Main 2025 Jan 29 Shift 1, Physics Q3: Simple Harmonic Motion And Oscillation

JEE Main2025Jan 29, Shift 1Physics

An electric dipole of mass $m$ , charge $q$ , and length $ℓ$ is placed in a uniform electric field $E = E_{0} \hat{i} .$ When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

A
$\frac{1}{2 π} \frac{2 m ℓ}{q E _{0}}$
B
$2 π \frac{m ℓ}{q E _{0}}$
C
$\frac{1}{2 π} \frac{m ℓ}{2 q E _{0}}$
D
$2 π \frac{m ℓ}{2 q E _{0}}$

Solution

$I ω^{2} θ = q ℓ E_{0} θ$

$2 m (\frac{ℓ}{2})^{2} ω^{2} = q ℓ E_{0}$

$ω^{2} = \frac{2 q E _{0}}{m ℓ}$

$T = 2 π \frac{m ℓ}{2 q E _{0}}$

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JEE Main 2025 Jan 29 Shift 1, Physics Q3: Simple Harmonic Motion And Oscillation

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