A pendulum suspended from the ceiling of a tr | vedclass

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Question

(A) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g_{eff}}}$,where $g_{eff}$ is the effective acceleration due to gravity.

Vedclass · Accepted Answer

$2\,s$

Vedclass · Answer

(A) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L}{g_{eff}}}$,where $g_{eff}$ is the effective acceleration due to gravity.When the train accelerates with $a = 10\,m/s^2$,the effective acceleration is $g_{eff} = \sqrt{g^2 + a^2}$.When the train retards with $a = 10\,m/s^2$,the effective acceleration is $g'_{eff} = \sqrt{g^2 + (-a)^2} = \sqrt{g^2 + a^2}$.Since the magnitude of the effective acceleration remains the same in both cases,the time period $T$ remains unchanged.Therefore,the time period is $2\,s$.

$A$ pendulum suspended from the ceiling of a train oscillates with a time period $2\,s$,when the train is accelerating at $10\,m/s^2$. What will be its time period when the train retards at $10\,m/s^2$?

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