Question

In a certain clock, a pendulum of length L1 has a period T1 = 0.95s. The length of the pendulum

is adjusted to a new value L2 such that T2 = 1.0 s. What is theratio L2/L1?

Answer 1

Ratio of length will be
`(L_2)/(L_1)=1.108`

Step-by-step explanation:

We have given time period of the pendulum when length is
`L_1` is
`T_1=0.95sec`

And when length is
`L_2` time period
`T_2=1sec`

We know that time period is given by

`T=2\pi \sqrt{(L)/(g)}`

So
`0.95=2\pi \sqrt{(L_1)/(g)}`----eqn 1

And
`1=2\pi \sqrt{(L_2)/(g)}`-------eqn 2

Dividing eqn 2 by eqn 1

`(1)/(0.95)=\sqrt{(L_2)/(L_1)}`

Squaring both side

`(L_2)/(L_1)=1.108`