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

Correct answer: D. θ_1 l_2=θ_2 l_1 aligned & ω= g & α=-ω^2 θ & ~g _1 θ_1= g _2 θ_2 & θ_1 _2=θ_2 _2 aligned

JEE Main 20254 AprilMorning Shift

JEE Main 2025 · 4 April · Morning Shift · Physics · Oscillations

Two simple pendulums having lengths l_1 and l_2 with negligible...

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. $\theta_1 l_2=\theta_2 l_1$

\begin{aligned} & \omega=\sqrt{\frac{\mathrm{g}}{\ell}} \\ & \alpha=-\omega^2 \theta \\ & \therefore \frac{\mathrm{~g}}{\ell_1} \theta_1=\frac{\mathrm{g}}{\ell_2} \theta_2 \\ & \Rightarrow \theta_1 \ell_2=\theta_2 \ell_2\end{aligned}