If T 1 = time period of a simple pendulum of infinite length, T 2 = time period of simple harmonic motion of a body dropped in a tunnel dug along diameter of earth and T 3 = time period of circu

Question

If T 1 ​ = time period of a simple pendulum of infinite length, T 2 ​ = time period of simple harmonic motion of a body dropped in a tunnel dug along diameter of earth and T 3 ​ = time period of circular motion of a satellite revolving near the surface of the earth, then:

TestHub · Accepted Answer

T 1 ​ = 2 π g ( ℓ 1 ​ + R 1 ​ ) 1 ​ = 2 π g R ​ ​ ​ ∴ ℓ → ∞ ​ T 2 ​ = ω 2 ​ 2 π ​ ​ F 2 ​ = R 3 − GmMx ​ ⇒ F 2 ​ = − mw 2 2 ​ x ​ ⇒ T 2 ​ = 2 π g R ​ ​ ​ ∴ T 3 ​ = 2 π g R ​ ​ ​

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