How the mass of the Earth can be determined?
Difficulty: Medium
Mass of the earth:
Consider a body of mass m on the surface of the Earth. Let the mass of the Earth be Me and the radius of the Earth be R. According to the law of gravitation, the gravitational force F of the Earth acting on a the the the the the the body is given by
$F=G \: m \frac{Me}{R^{2}}$ …………. (i)
But the force with which Earth attracts a body
towards its center is equal to its weight W.
Therefore,
F = W = mg
$mg= \:G \: m \frac{Me}{R^{2}}$
$g= \:G \: \frac{Me}{R^{2}}$
and $Me=R^{2}\frac{g}{G}$
Mass $M\epsilon$ of the Earth can be determined on putting the values in equation
$Me=\left(6.4\times10^{6}m\right)^{2}\times\frac{10ms^{-2}}{6.673}\times10^{-11}Nm^{2}kg^{-2}$
$=6.0\times10^{24}kg$
Thus, the mass of the Earth is $=6.0\times10^{24}kg$
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