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

(D) $\theta_{1} l_{2}=\theta_{2} l_{1}$

(A) $\theta_{1} l_{2}^{2}=\theta_{2} l_{1}^{2}$

(B) $\theta_{1} l_{1}=\theta_{2} l_{2}$

(C) $\theta_{1} l_{1}^{2}=\theta_{2} l_{2}^{2}$

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Elasticity & SHM

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?

Answer: (D)

For small oscillations the angular acceleration of a simple pendulum is

α = - \frac{g}{l} θ

. Setting the two accelerations equal,

\frac{g}{l _{1}} θ_{1} = \frac{g}{l _{2}} θ_{2} \Rightarrow θ_{1} l_{2} = θ_{2} l_{1} .

The displacements and lengths satisfy

θ_{1} l_{2} = θ_{2} l_{1}

JEE Main · 2025 · 04 Apr 2025 · Shift 1 · Single correct option