Q. 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
Explanation
(b) 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
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.