Qstnid -I-17-a Plumb Bob Is Hung From The Ceiling Of A Train Compartment. If The Train Moves With An Acceleration &Lsquo;a‘ Along A Straight Horizontal Track , The String Supporting The Bob Makes An Angle Tan<sup>-1</sup> (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<sup>-1</sup> (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 Accelerating On A Horizontal Straight Track Or Moving On An Incline? If Yes, How? If Not, Then Suggest A Method To Do So. - 05: Newton's Laws Of Motion

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#17
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 accelerating on a horizontal straight track or moving on an incline? If yes, how? If not, then suggest a method to do so.
Ans : No, a person sitting inside the compartment can't tell just by looking at the plumb line whether the train is accelerating on a horizontal straight track or moving on an incline.
When the train is accelerating along the horizontal, the tension in the string is `` m\sqrt{{g}^{2}+{a}^{2}}``; when it is moving on the inclined plane, the tension is mg. So, by measuring the tension in the string we can differentiate between the two cases.