First slide

Acceeleration due to gravity on surface of planet

Question

Average density of the earth

Moderate

A

does not depend on g
B

is a complex function of g
C

is directly proportional to g
D

is inversely proportional to g

Solution

We know that,
$\begin{array}{l} g = \frac{GM}{R^{2}} where M = (\frac{4}{3} {πR}^{3}) ρ \\ ∴ g = \frac{G}{R^{2}} (\frac{4}{3} {πR}^{3}) ρ = (\frac{4 GπR}{3}) ρ \\ or g \propto ρ or ρ \propto g \end{array}$

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