Q 11-13-158JEE MainJEE Main 2025 (4 Apr, Shift 1)Easy
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 the same, then which expression is correct?
Answer: (D) $\theta_1l_2 = \theta_2l_1$
For small oscillations of a simple pendulum, $\alpha = -\dfrac gl\theta$. Equal magnitudes of angular acceleration give
$$\frac{g}{l_1}\theta_1 = \frac{g}{l_2}\theta_2 \Rightarrow \theta_1l_2 = \theta_2l_1$$
Solution by Sreeraj P, M.Sc Physics