Question : A pendulum suspended from the ceiling of a train has a period T, when the train is at rest. When the train is accelerating with a uniform acceleration 'a', the period of oscillation will :
(A) Increase
(B) Decrease
(C) Remains unaffected
(D) Becomes Infinite
Doubt by Girisha
Solution :
When the train will accelerate with uniform acceleration then in spite of force of gravity in the vertical direction the train will also experience an extra force in the horizontal direction which is opposite the direction in which the train is accelerating.
So there will be two accelerations in the perpendicular directions - one (g) due to gravity in the vertical direction while the other (a) in horizontal direction due to the acceleration of the train.
So the effective acceleration will be given by vector sum of these two accelerations.
a'>g
so when the magnitude of acceleration increases then the time period will decrease.
Hence, (B) Decrease, would be the correct option.
Note : In case the train decelerates even then the time period of the pendulum will decrease beacuse only the direction of net acceleration will change but the magnitude will remain same. The time period of the pendulum depends on the magnitude of the net acceleration not on its direction.