Q 11-06-126JEE MainJEE Main 2023 (10 Apr, Shift 1)Medium
If the earth suddenly shrinks to $\dfrac1{64}$th of its original volume with its mass remaining the same, the period of rotation of earth becomes $\dfrac{24}{x}$ h. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 16
Volume $\dfrac1{64}$ means radius $\dfrac R4$, so $I\propto R^2$ becomes $\dfrac I{16}$. Angular momentum is conserved, so $\omega$ becomes $16\omega$ and $T=\dfrac{24}{16}$ h. $x=16$.
Solution by Sreeraj P, M.Sc Physics