Question

Assuming the radius of the earth to be $6.38\times {10}^{8}cm$, the gravitational constant to be $6.67\times {10}^{-}8c{m}^3/g{s}^2$ , acceleration due to gravity on the surface to be $980cm/s^2$, find the mean density (in $-g/c{m}^3$) of the earth.

Answer 1

Weight, mg$=\frac{GMm}{R^2}$

$M=\frac{4}{3}\pi R^3\rho$

$\rho =\frac{3g}{4\pi GR}$

$=\frac{3\times 980}{4\pi \times 6.67\times {10}^{-}8\times 6.38\times {10}^8}$

$=5.49g/c{m}^3$