Q68 / 90 · JEE Main 2024 (27 Jan Shift 1) · Physics

The acceleration due to gravity on the surface of earth is $g$ . If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

Solution

The acceleration due to gravity is related to the mass and the radius of the Earth by the formula:

$g = \frac{G M}{R^{2}} \Rightarrow g \propto \frac{1}{R^{2}} . . . (1)$

Thus, from equation (1), it follows that

$\frac{g_{2}}{g_{1}} = \frac{R_{1}^{2}}{R_{2}^{2}} = \frac{R_{1}^{2}}{{(\frac{R_{1}}{2})}^{2}} = 4 \Rightarrow g_{2} = 4 g$

Hence, the correct answer is option: 'D'.