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  • The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below  </

The dependence of acceleration due to gravity g on the distance r from the centre of the earth, assumed to be a sphere of radius R of uniform density is as shown in figures below

 

The correct figure is

Option: 1

(4)


Option: 2

(1)


Option: 3

(2)


Option: 4

(3)


Answers (1)

best_answer

\\ \text{The acceleration due to gravity at a depth d below the surface of earth is}\\ g^{\prime}=g\left(1-\frac{d}{R}\right)=$ $g\left(\frac{R-d}{R}\right)=g \frac{r}{R}$----------(i) \\ where R-d=r=distance of location from the centre of the earth. \\ When $r=0, g^{\prime}=0$ \\ From (i), $g \propto r$ till $\mathrm{R}=r,$ for which $g^{\prime}=g$ \\ For $r>R, g^{\prime}=\frac{g R^{2}}{(R+h)^{2}}=\frac{g R^{2}}{r^{2}}$ or $g^{\prime} \propto \frac{1}{r^{2}} \ \\ Here, \ $R+h=r$ \\

Therefore, the variation of g with distance r from centre of earth will be as shown in figure (4).

Posted by

Ritika Jonwal

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