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Q. Amongst the following the average density of the earth

NTA AbhyasNTA Abhyas 2020

Solution:

$Acceleration \, due \, to \, gravity \, g=\frac{G M}{R^{2}}, \, \, \, M=\left(\frac{4}{3} \pi R^{3}\right)\rho $
$∴ \, g=\frac{4 G}{3}\frac{\pi R^{3}}{R^{2}}\rho $
$\Longrightarrow \, g=\left(\frac{4 G \pi R}{3}\right)\rho \, \left(\rho = a v e r a g e \, d e n s i t y\right)$
$\Longrightarrow g∝\rho \, or \, \rho ∝g \, \, $