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  • Calculate the average density of the earth in terms of g, G and R.

Calculate the average density of the earth in terms of g, G and R.

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The weight of an object is nothing but the gravitational force by the earth on that body.

By universal law of gravitation, if two particles of mass m1 and m2 are kept at a separation then the gravitational force between them will be given as:

F= \frac{Gm_{1}m_{2}}{r^{2}}
The weight is generally given as mg, therefore:

mg= \frac{GM_{e}m}{R_{e}^{2}}\\ \Rightarrow g= \frac{GM_{e}}{R_{e}^{2}}\\

If density of earth is d, its mass can be calculated by using the fact: mass is product of density and volume.

M_{e}=d \times \frac{4\pi\left ( R_{e} \right )^{3} }{3}

BY putting the value of mass:

\Rightarrow g=\frac{G}{R_{e}^{2}}\left ( d \times \frac{4 \pi \left ( R_{e} \right )^{3}}{3} \right )\\ \Rightarrow g=\frac{G}{1}\left ( d \times \frac{4 \pi \left ( R_{e} \right )}{3} \right )\\ \Rightarrow g=\frac{4 \pi dG\left ( R_{e} \right )}{3}\\ \Rightarrow d=\frac{3g}{4 \pi G\left ( R_{e} \right )}\\

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