Consider the following four periods: (i) Tₛₜ: period of a satellite just above Earth's surface; (ii) Tₘₐ: period of oscillation through a diameter tunnel in a uniform Earth; (iii) Tₛₚ: period of a simple pendulum of length equal to Earth's radius in a uniform field g; (iv) Tᵢₛ: period of an infinitely long simple pendulum in Earth's actual gravitational field. Which relation is correct?
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Question

Consider the following four periods: (i) Tₛₜ: period of a satellite just above Earth's surface; (ii) Tₘₐ: period of oscillation through a diameter tunnel in a uniform Earth; (iii) Tₛₚ: period of a simple pendulum of length equal to Earth's radius in a uniform field g; (iv) Tᵢₛ: period of an infinitely long simple pendulum in Earth's actual gravitational field. Which relation is correct?

Options

G1 Physics · Accepted Answer

For a satellite just above Earth's surface, Tₛₜ = 2π√(R/g). For SHM in a diameter tunnel of a uniform Earth, Tₘₐ = 2π√(R/g). For a pendulum of length R in uniform field g, Tₛₚ = 2π√(R/g). For an infinitely long pendulum in Earth's actual field, the limiting period is larger than Tₛₚ. Therefore Tₛₚ < Tᵢₛ. Correct answer: C.