The value of g is 4.0 $ms^{-2}$ at a distance of 10000 km from the center of the Earth. Find the mass of the Earth. ($5.99 \times 10^{24}$ kg)
Difficulty: Medium
Solution:
Gravitational acceleration = g = 4.0 $ms^{-2}$
Radius of Earth = $R_{e}$ = 10000 km = $10000 \times 1000$ m = $10^{7}$m
Mass of Earth = $M_{e}$ =?
$M_{e}$ =$\frac{(gR^{2})}{G}$
$M_{e}$ = $\frac{(4.0 \times (10^{7})^{2})}{(6.673 \times 10^{-11})}$
=$\frac{(4.0\times 10^{14})}{(6.673 \times 10^{-11})}$
= $0.599\times10^{25}$ kg = $5.99\times 10^{24}$ kg
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