question_answer

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                                    [CPMT 1983]

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

Correct Answer: B

Solution :

                   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.