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  • If the acceleration due to gravity inside the earth is to be kept constant, then the relation between the density d and the distance r from the centre of earth will be -

If the acceleration due to gravity inside the earth is to be kept constant, then the relation between the density d and the distance r from the centre of earth will be -

Option: 1

d \propto r


Option: 2

d \propto r^{1 / 2} \\


Option: 3

d \propto 1 / r \\


Option: 4

d \propto \frac{1}{r^{2}}


Answers (1)

best_answer

\begin{array}{l} g=\frac{G M}{m^{2}} \\ \text { Now, } m=\frac{4}{3} \pi r^{3} d \quad[d \rightarrow \text { density }] \\ \\ \therefore g=\frac{4 G \pi r^{3} d}{3 r^{2}}=\frac{4}{3} G \pi r d \\ \\ \Rightarrow d=\frac{3 g}{4 G \pi r} \\ \\ \text { or, } d \propto \frac{1}{R} \end{array}

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vinayak

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