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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?

Respuesta :

Answer:

Ratio of length will be [tex]\frac{L_2}{L_1}=1.108[/tex]

Explanation:

We have given time period of the pendulum when length is [tex]L_1[/tex] is [tex]T_1=0.95sec[/tex]

And when length is [tex]L_2[/tex] time period [tex]T_2=1sec[/tex]

We know that time period is given by

[tex]T=2\pi \sqrt{\frac{L}{g}}[/tex]

So [tex]0.95=2\pi \sqrt{\frac{L_1}{g}}[/tex]----eqn 1

And [tex]1=2\pi \sqrt{\frac{L_2}{g}}[/tex]-------eqn 2

Dividing eqn 2 by eqn 1

[tex]\frac{1}{0.95}=\sqrt{\frac{L_2}{L_1}}[/tex]

Squaring both side

[tex]\frac{L_2}{L_1}=1.108[/tex]

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