MCQ
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?
  • A
    $\theta_{1} l_{2}^{2}=\theta_{2} l_{1}^{2}$
  • B
    $\theta_{1} l_{1}=\theta_{2} l_{2}$
  • C
    $\theta_{1} l_{1}^{2}=\theta_{2} l_{2}^{2}$
  • $\theta_{1} l_{2}=\theta_{2} l_{1}$

Answer

Correct option: D.
$\theta_{1} l_{2}=\theta_{2} l_{1}$
(D) $\theta_{1} l_{2}=\theta_{2} l_{1}$
$\omega=\sqrt{\frac{\mathrm{g}}{\ell}}$
$\alpha=-\omega^{2} \theta$
$\therefore \frac{\mathrm{g}}{\ell_{1}} \theta_{1}=\frac{\mathrm{g}}{\ell_{2}} \theta_{2}$
$\Rightarrow \theta_{1} \ell_{2}=\theta_{2} \ell_{2}$

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