Q 11-13-031NEETJEE MainMedium
A tunnel is dug along a diameter of the Earth. A ball dropped into it would perform SHM. Its period is about (radius of Earth $= 6.4 \times 10^6$ m, $g = 10\ \text{m/s}^2$)
Answer: (A) $84$ minutes
Concept. Inside the Earth $g' = g\dfrac{r}{R}$, a restoring force proportional to $r$: SHM with $\omega^2 = \dfrac{g}{R}$.
Step 1. Period.
$$T = 2\pi\sqrt{\frac{6.4 \times 10^6}{10}} = 2\pi \times 800 \approx 5030\ \text{s} \approx 84\ \text{min}$$
Answer. $84$ minutes (Option A).
Solution by Sreeraj P, M.Sc Physics