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Question:

A simple pendulum is setup 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 with the vertical is

tan⁻¹(a/g) in the forward direction

tan⁻¹(a/g) in the forward direction

tan⁻¹(a/g) in the backward direction

tan⁻¹(a/g) in the backward direction

Solution:

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 = tan⁻¹(Fx/Fy) = tan⁻¹(ma/mg) = tan⁻¹(a/g) in backward direction