Question

A simple pendulum is setup in a trolly 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 with the vertical is

• 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

The correct option is B ${\tan }^{-1}\frac{a}{g}$ in the backward direction

Due to horizontal acceleration, a pseudo force $ma$ acts on the bob of pendulum in horizontal direction, backwards. Also the gravitational force $mg$ acts on it vertically downwards.

Hence the angle that the thread makes with the vertical $=ta{n}^{-1}\left(\frac{F_x}{F_y}\right)$ $=ta{n}^{-1}\left(\frac{ma}{mg}\right)$ $=ta{n}^{-1}\left(\frac{a}{g}\right)$ in backward direction