A plumb bob is hung from the ceiling of a train compartment. If the train moves with an acceleration ‘a’ along a straight horizontal track, the string supporting the bob makes an angle tan-1 (a/g) with the normal to the ceiling. Suppose the train moves on an inclined straight track with uniform velocity. If the angle of incline is tan-1 (a/g). the string again makes the same angle with the normal to the ceiling. Can a person sitting inside the compartment tell by looking at the plumb line whether the train is accelerated on a horizontal straight track or it is going on an incline? If yes, how? If no, suggest a method to do so.
In both of the cases the angle that string makes with normal to the ceiling is same. Therefore, a person sitting inside the compartment cannot tell by looking at the plumb line whether the train is accelerated on a horizontal track or it is going on an incline. To determine this, he should know the weight of the bob and measure the tension in the string with a spring balance.
a
Since, 
rain on an incline with uniform velocity
T = W
If the tension and the weight of the bob are same then the train is going with uniform velocity on an incline. If the tension in the string is more than the weight of the bob, the train is moving on a horizontal track with acceleration.