Q 11-07-145JEE MainJEE Main 2021 (18 Mar, Shift 2)Easy
If the angular velocity of earth's spin is increased such that the bodies at the equator start floating, the duration of the day would be approximately:
(Take: $g = 10\ \text{m s}^{-2}$, the radius of earth, $R = 6400\times10^3$ m, Take $\pi = 3.14$)
Answer: (D) 84 minutes
Bodies float when $\omega^2R = g$:
$$T = 2\pi\sqrt{\frac{R}{g}} = 2\times3.14\sqrt{\frac{6.4\times10^6}{10}} = 6.28\times800 = 5024\ \text{s} \approx 84\ \text{minutes}$$
Solution by Sreeraj P, M.Sc Physics