A) Increase in mass
B) Increase in radius
C) Both affect the attraction equally
D) None of the above
Correct Answer: B
Solution :
The relation between mass and density of earth is given from Newton's law of gravitation, according to which \[{{M}_{e}}=\frac{gR_{e}^{2}}{G}\] where \[{{M}_{e}}\] is mass of earth, G the gravitational constant, \[{{R}_{e}}\] the radius of earth and g the I acceleration due to gravity. Also, \[mass=volume\times density\] \[\therefore \] \[g=\frac{G\times volume\times density}{{{R}^{2}}}\] Assuming spherical shape of earth volume \[=\frac{4}{3}\pi {{R}^{3}}\] \[g=G\times \frac{4}{3}\frac{\pi {{R}^{3}}}{{{R}^{2}}}\rho \] \[\Rightarrow \] \[g=G.\frac{4}{3}\pi R\rho \] Hence, increase in radius would dominate.
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