Question

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

Answer 1

Answer: (B)

$\tan^{- 1}\frac{a}{g}$ in the backward direction

Answer 2

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.