Q 11-07-051JEE MainJEE Main 2025 (24 Jan, Shift 2)Easy
Acceleration due to gravity on the surface of earth is $g$. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ______ $g$.
Numerical value type. Enter your answer.
Answer: 9
$g = \dfrac{GM}{R^2}$. With $M$ fixed and $R \to R/3$:
$$g' = \frac{GM}{(R/3)^2} = 9\,\frac{GM}{R^2} = 9g$$
Solution by Sreeraj P, M.Sc Physics