5. Two pendulums of lengths L₁ and L2 and when located at the respective distances R₁ and R₂ from the center of the earth -have periods p₁ and P2. Show that P₁_R₁L₁ R₂√L₂ = P2 Assume that the differential equation of a simple pendulum of length L is LO"+ge = 0, where g = GM/R2 is the gravitational acceleration at the location of the pendulum (at distance R from the center of the earth; M denotes the mass of the earth).
5. Two pendulums of lengths L₁ and L2 and when located at the respective distances R₁ and R₂ from the center of the earth -have periods p₁ and P2. Show that P₁_R₁L₁ R₂√L₂ = P2 Assume that the differential equation of a simple pendulum of length L is LO"+ge = 0, where g = GM/R2 is the gravitational acceleration at the location of the pendulum (at distance R from the center of the earth; M denotes the mass of the earth).
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Transcribed Image Text:5. Two pendulums of lengths L₁ and L2 and when located at the respective distances R₁
and R₂ from the center of the earth -have periods p₁ and P2. Show that
P₁_R₁L₁
R₂√L₂
P2
=
Assume that the differential equation of a simple pendulum of length L is LO"+ge = 0,
where g =
GM/R2 is the gravitational acceleration at the location of the pendulum
(at distance R from the center of the earth; M denotes the mass of the earth).
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