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

Options

A. `"tan"^(-1)(g)/(a)` in the forward direction
B. `"tan"^(-1)(g)/(a)` in the backward direction
C. `"tan"^(-1)(a)/(g)` in the backward direction
D. `"tan"^(-1)(a)/(g)` in the forward direction

Answer

C

Explanation

The trolley is moving towards right with an acceleration a . As the pendulum is in an accelerated frame of reference, a fictious force ma acts on the bob in the backward direction. The thread makes an angle `theta` with the vertical, such that `"tan" theta =(ma)/(mg)=(a)/(g) or theta ="tan"^(-1) ((a)/(g))` in the backward direction.