Tunnel Through EarthHardQuestion 31158
Question
A particle dropped into a tunnel through the centre of Earth oscillates with period:
- A2π√(R/g)Correct
- B2π√(R/(2g))
- Cπ√(R/g)
- D√(2πR/g)
Correct answer
2π√(R/g)
Explanation
Inside Earth, g(r) = gr/R. This is SHM with ω² = g/R. T = 2π/ω = 2π√(R/g) ≈ 84 min — equal to orbital period at Earth's surface!