Question

Periodic time of a simple pendulum suspended in stationary lift is T. Now when lift moves in upward direction with acceleration g 3 . New periodic time will be …………​

Answer 1

Given:

Periodic time of a simple pendulum suspended in stationary lift is T. Now, lift moves in upward direction with acceleration g/3.

To find:

New time period?

Calculation:

Initially, when lift is stationary :

$\rm \: T = 2\pi \sqrt{ \dfrac{l}{g} }$

Now, when lift is moving with g/3 upwards, net force on pendulum bob = g + g/3 = 4g/3.

$\rm \implies \: T_{2} = 2\pi \sqrt{ \dfrac{l}{( \frac{4g}{3} )} }$

$\rm \implies \: T_{2} = 2\pi \sqrt{ \dfrac{3l}{4g} }$

$\rm \implies \: T_{2} = \dfrac{ \sqrt{3} }{2} \times 2\pi \sqrt{ \dfrac{l}{g} }$

$\rm \implies \: T_{2} = \dfrac{ \sqrt{3} }{2} \times \: T$

$\rm \implies \: T_{2} = \dfrac{ T\sqrt{3} }{2}$

So, new time period is (T√3)/2 .