MHT CET · Physics · Gravitation
The average density of the earth is [ \(\mathrm{g}\) is acceleration due to gravity]
- A inversely proportional to \(\mathrm{g}^2\)
- B directly proportional to \(g\)
- C inversely proportional to \(\mathrm{g}\)
- D directly proportional to \(\mathrm{g}^2\)
Answer & Solution
Correct Answer
(B) directly proportional to \(g\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{\mathrm{G}}{\mathrm{R}^2} \cdot \frac{4}{3} \pi \mathrm{R}^3 \cdot \rho=\mathrm{G} \frac{4}{3} \cdot \pi \mathrm{R} \rho \\ & \therefore \mathrm{g} \propto \rho\end{aligned}\)
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