The average density of the earth is [ $\mathrm{g}$ is acceleration due to gravity]

The average density of the earth is [ $\mathrm{g}$ is acceleration due to gravity]
  1. inversely proportional to $\mathrm{g}^2$
  2. directly proportional to $g$
  3. inversely proportional to $\mathrm{g}$
  4. directly proportional to $\mathrm{g}^2$

Solution

$\begin{aligned} & \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{\mathrm{G}}{\mathrm{R}^2} \cdot \frac{4}{3} \pi \mathrm{R}^3 \cdot \rho=\mathrm{G} \frac{4}{3} \cdot \pi \mathrm{R} \rho \\ & \therefore \mathrm{g} \propto \rho\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 2)

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