Find the Time period of oscillation ( in sec ) of an infinite pendulum, which is hovering just above the surface of the Earth.
Note:
An
Infinite
Pendulum is a obviously
infinitely
long. The Hinge of the Pendulum is at
infinite
distance from the surface of the Earth.
Also, note that the
all
the mass of the pendulum is concentrated at the bottom of the pendulum, where the bob is situated (in other words, the mass is not uniformly distributed...Its more like a stone tied at the end of a massless string)
Details and Assumptions:
Assume that the oscillations are very small.
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for a pendulum having infinite length we have Time period = 2 * pi root(1/g(1/L + 1/R) where L tends to infinite so then it becomes T = 2 * pi root (R/g) = 5077.58 secs.