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A grandfather clock keeps time using a pendulum consisting of a light rod connected to a small heavy mass. With a rod of length L, the period of oscillation is 2.00 s. What should the length of the rod be for the period of the oscillations to be 1.00 s?

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Answer:

The length of the rod should be

[tex]\frac{L}{4} \\ [/tex]

Explanation:

Period of simple pendulum is given by

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

We have

[tex]\frac{T_1^2}{T_2^2}=\frac{l_1}{l_2}\\\\\frac{2^2}{1^2}=\frac{L}{l_2}\\\\l_2=\frac{L}{4} \\ [/tex]

The length of the rod should be

[tex]\frac{L}{4} \\ [/tex]

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