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  • The length of a second’s pendulum on the surface of earth is 1 m. What will be the length of a second’s pendulum on the moon?

The length of a second’s pendulum on the surface of earth is 1 m. What will be the length of a second’s pendulum on the moon?

 

Answers (1)

A second pendulum is a pendulum with time period (T) = 2 seconds

T_{e} = 2\pi\sqrt{\frac{ l_{e}}{g_{e}}} 

Thus, T_{e}^{2} = 4\pi ^{2}{\frac{l_{e}}{g_{e}}}     …… (i)

Now, T_m = 2\pi \sqrt{ \frac{l_{m}}{g_{m}}}

Thus, T_{m}^{2} = 4\pi ^{2} 6\frac{ lm}{g_e}        ……. (ii)   (gm=ge/6)

Now, for the second pendulum,

\frac{T_{m}^{2}}{T_{e}^{2}}= {6g_e} \frac{l_{e}}{g_{e}l_m}

1 = \frac{6lm}{l_{e}}

1 = \frac{6l_{m}}{1m}   ……. (since l_{e}=1m)

Thus, l_{m} = \frac{1}{6} m

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infoexpert24

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