Question

A mass is suspended from the ceiling of a train carriage by a string. The string makes an angle θ with the vertical when the train is accelerating along a straight horizontal track. What is the acceleration of the train in terms of gravitational acceleration?

Answer 1

From the frame of reference of train, there is pseudo force of ma on bob in backward direction.

Balancing force in horizontal direction, Tsinθ=ma

Balancing force in vertical direction, Tcosθ=mg

Taking ratio,

cosθ

sinθ

= ga

⟹tanθ= ga

⟹θ=tan

−1ga..........

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