Question

A simple pendulum in a stationary lift has time period T.What would be the effect on the time period when the life
1)Moves up with uniform velocity
2)Moves down with uniform velocity
3)Moves up with uniform acceleration
4)Moves down with inform acceleration
5)Begins to fall freely under gravity?​

Answer 1

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Question:-

A simple pendulum in a stationary life has time period T. What would be the effect on the time period when the lift

1)Moves up with uniform velocity

2)Moves down with uniform velocity

3)Moves up with uniform acceleration

4)Moves down with uniform acceleration

5)Begins to fall freely under gravity?

Answer:-

Given,

• A simple pendulum in a stationary life has time period =T

To Find,

• Effects on the time period when the life in given above conditions.

Now,

Let's consider 1st condition:-

• When the lift moves up with uniform velocity i.e., a =0 there would be no change in the time period of the simple pendulum.

Let's consider 2nd condition:-

• When the lift moves down with uniform velocity i.e a=0 there would be no change in the time period of the simple pendulum.

Let's consider 3rd condition:-

• When lift is moving with acceleration "a" then relative acceleration = g+a

Time period

$t = 2\pi \sqrt{ \frac{l}{g + a} }$

so,

when lift is moving up with uniform acceleration time period of pendulum in it decreases.

Let's consider 4th condition:-

• When lift is moving down with acceleration 'a' then relative acceleration = g-a

Time period

$t = 2\pi \sqrt{ \frac{l}{g - a} }$

so,

When lift is moving down with acceleration, time period of pendulum in it increases.

Let's consider 5th condition:-

• When the lift begins to fall freely under gravity , a=g then the time period if a simple pendulum becomes infinite.

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