Physics - Gravitation Question with Solution | TestHub

$\text{Density}=\frac{\text{Mass of earth}}{\text{Volume of earth}}$

$\rho =\frac{\mathit{\text{M}}}{\left(4/3\right)\pi {\mathit{\text{R}}}^3}=\frac{3\mathit{\text{M}}}{4\pi {\mathit{\text{R}}}^3}$..........(i)

$g=\frac{\mathit{\text{GM}}}{{\mathit{\text{R}}}^2}$...........(ii)

$\therefore$$\frac{\rho }{g}=\frac{3\mathit{\text{M}}}{4\pi {\mathit{\text{R}}}^3}\times \frac{{\mathit{\text{R}}}^2}{\mathit{\text{GM}}}=\frac{3}{4\pi \mathit{\text{RG}}}$or$\rho =\frac{3}{4\pi \mathit{\text{RG}}}g$

$\therefore$The average density is directly proportional to$g$.