A person measures a time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration g 3 , the time period of the pendulum w

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A person measures a time period of a simple pendulum inside a stationary lift and finds it to be T. If the lift starts accelerating upwards with an acceleration g 3 , the time period of the pendulum will be

TestHub · Accepted Answer

Time period of simple pendulum inside a stationary lift,
$T = 2 π \sqrt{\frac{l}{g}}$ … (i)
Where, $l$ = length of string
and g = gravitational acceleration
Acceleration of lift in upward direction,
$a = \frac{g}{3}$
$∴$ Time period of pendulum,
$T^{'} = 2 π \sqrt{\frac{l}{g + a}} = 2 π \sqrt{\frac{l}{g + \frac{g}{3}}}$
$= 2 π \sqrt{\frac{3 l}{4 g}} = 2 π . \frac{\sqrt{3}}{2} . \sqrt{\frac{l}{g}}$
$= \frac{\sqrt{3}}{2} . 2 π \sqrt{\frac{l}{g}} = \frac{\sqrt{3}}{2} T$ [from Eq. (i)]

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