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)

In accelerated frame of reference, a fictitious
force (pseudo force) $ma$ acts on the bob of pendulum as shown in figure.

Hence, $tan\theta =\frac{ma}{mg}=\frac{a}{g}\Rightarrow \theta =\left(tan\right)^{- 1}\left(\frac{a}{g}\right)$ in the
backward direction.