Question

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?

Answer 1

The length of the rod should be

`(L)/(4) \\`

Step-by-step explanation:

Period of simple pendulum is given by

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

We have

`(T_1^2)/(T_2^2)=(l_1)/(l_2)\\\\(2^2)/(1^2)=(L)/(l_2)\\\\l_2=(L)/(4) \\`

The length of the rod should be

`(L)/(4) \\`