Q 11-06-084JEE MainJEE Main 2024 (6 Apr, Shift 1)Medium
If the radius of the earth is reduced to three-fourths of its present value without change in its mass, then the duration of the day on earth will be ______ hours 30 minutes.
Numerical value type. Enter your answer.
Answer: 13
Angular momentum is conserved: $I\omega = \text{constant}$ with $I \propto R^2$, so $T \propto R^2$.
$$T' = 24\times\left(\frac34\right)^2 = 24\times\frac{9}{16} = 13.5\ \text{h} = 13\ \text{h}\ 30\ \text{min}$$
Solution by Sreeraj P, M.Sc Physics