JEE PYQ: Gravitation Question 6
Question 6 - 2021 (18 Mar Shift 2)
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: $g = 10$ ms$^{-2}$, the radius of earth, $R = 6400 \times 10^3$ m, Take $\pi = 3.14$)
(1) 60 minutes
(2) does not change
(3) 1200 minutes
(4) 84 minutes
Show Answer
Answer: (4)
Solution
For floating at equator: $mg = m\omega^2 R$, so $\omega = \sqrt{g/R}$. $T = \frac{2\pi}{\omega} = 2\pi\sqrt{R/g} = 2\pi\sqrt{\frac{6400 \times 10^3}{10}} \approx 5027$ s $\approx 84$ minutes.
BETA
