A plumb line is hanging from the ceiling of a train. If the train moving along a horizontal track with a uniform acceleration a, the plumb line gets inclined to the vertical at an angle $\theta$ is given by 

When the train is at rest or moving with a uniform velocity, the plumb line hangs vertically along OB . If the train moves with an acceleration a, the plumb line gets inclined along OC, the direction of the resultant of accelerations a and g. It is clear from the figure that $\tan \mathrm{\theta }=\frac{a}{g}$.