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# A pendulum suspended from the roof of a train has a period T (When the train is at rest). When the train is accelerating with a uniform acceleration ‘a’, the time period of the pendulum will (a) Increase (b) Decrease (c) Remain unaffected (d) Become infinite

Arun
25768 Points
11 months ago
When a train is moving with acceleration, the pendulum is exerted by a pseudo acceleration opposite to the direction of the train. As a result, there will be an increase in effective acceleration on the pendulum. The time period will decrease as the time period is inversely proportional to the square root of effective acceleration.

vaibhav patil
18 Points
11 months ago
t=​$t=sqrtl/g+a(cotTheta)$ is time period  and it veries always
m​​w2x=mgsintheata+macostheata
w2x=gsin(theata)+acos(theata)
and x=l×theata....................as per small theat theata=sintheata
w2l×theata=gtheata+acostheata
w2l=g+acostheata÷theata
w2=g+acot theata.......................as per theata is very small(theata=sintheata)
w=$sqrt{l\g+acot(Theta) }$
and
t=2$2pi \sqrt{l/g+acostheata}$
so the time period is veriable
Vikas TU
14148 Points
11 months ago
If it is accelerating horizontally, the pendulum will think it feels a gravity of
sqrt(g^2+a^2) so the period would decrease by a factor of (1+(a/g)^2)^(-1/4)