Acceleration due to gravity on the surface of earth is ' $g$. If the diameter of earth is reduced to

Question

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.\

Professor PC Thomas Classes · Answer

(9) : Acceleration due to gravity on the surface of earth, $g=\frac{G M_{e}}{R_{e}^{2}}$\ where ' $M_{e}$ ' is mass of earth, ' $R_{e}$ ' is radius of earth.\ If diameter of earth reduced to on third, then radius would also reduced to third.\ Hence, $g^{\prime}=\frac{G M_{e}}{\left(\frac{R_{e}}{3}ight)^{2}}=\frac{9 G M_{e}}{R_{e}{ }^{2}}=9 g$