JEE Main 2025 Apr 4 Shift 1, Physics Q17: SHM in Pendulums

JEE Main2025Apr 4, Shift 1Physics

Two simple pendulums having lengths $l_{1}$ and $l_{2}$ with negligible string mass undergo angular displacements $θ_{1}$ and $θ_{2}$ , from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?

A
$θ_{1} l_{2}^{2} = θ_{2} l_{1}^{2}$
B
$θ_{1} l_{1} = θ_{2} l_{2}$
C
$θ_{1} l_{1}^{2} = θ_{2} l_{2}^{2}$
D
$θ_{1} l_{2} = θ_{2} l_{1}$

Solution

For small oscillations of a simple pendulum, the equation of motion is $\ddot{θ} = - \frac{g}{l} θ$ . So the magnitude of angular acceleration at displacement $θ$ is $α = \frac{g θ}{l}$ .

Setting the magnitudes equal for the two pendulums: $\frac{g θ _{1}}{l _{1}} = \frac{g θ _{2}}{l _{2}}$ , i.e. $θ_{1} l_{2} = θ_{2} l_{1}$ .

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JEE Main 2025 Apr 4 Shift 1, Physics Q17: SHM in Pendulums

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