A simple pendulum is set up in a trolley which moves to the right with an acceleration a on a horizontal plane. Then the thread of the pendulum in the mean position makes an angle $\theta$ with the vertical
(a) $\tan^{-1} \frac{a}{g}$ in the forward direction (b) $\tan^{-1} \frac{a}{g}$ in the backward direction (c) $\tan^{-1} \frac{g}{a}$ in the backward direction (d) $\tan^{-1} \frac{g}{a}$ in the forward direction
Text Solution
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In accelerated frame of reference, a fictitious force (pseudo force) ma acts on the bob of pendulum as shown in figure.
Hence, $\tan \theta = \frac{ma}{mg} = \frac{a}{g} \Rightarrow \theta = \tan^{-1} \left(\frac{a}{g}\right)$ in the backward direction.
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