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

Question

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 :

TestHub · Accepted Answer

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

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

Physics - Gravitation Question with Solution | TestHub

Options:

Doubts & Discussion