Gravity Pendulum mania
Classical Mechanics
Level
2
A simple pendulum has a time period T on the surface of the Earth, and T' when taken to a height R above the surface of the Earth, where R is the radius of the Earth.
What is the value of T'/T?
The answer is 2.
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1 solution
From the equation of pendulum, T = 2 π g L you can make it so simple.
Here, the g is decreased as you rise up to a height, R , which equal to the Radius of the earth. So you can simplify it by saying, Radius is Doubled And you know g = ( R + h ) 2 G M So as g is Inversely Proportional to the square of distance from the center. So as that Distance is doubled, g is decreased 2 2 = 4 times.
And Time period is inversely proportional to the square root of g . So as g is decreased by 4, New Time period, T' is increased 4 = 2 times.
And that's how you get T T ′ = 2 Its so simple, isn't it!