If the intensity of gravitational field at all places inside earth is presumed to be constant, then the relation between the density of earth $(ρ)$ and distance $(r)$ from the centre of the earth will be :

ρ \propto r

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ρ \propto \frac{1}{r}

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ρ \propto \sqrt{r}

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ρ \propto \frac{1}{\sqrt{r}}

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Solution

The correct option is C $ρ \propto \frac{1}{r}$
Gravitational field intensity $E_{G}$ is given by
$E_{G} = \frac{G M}{r^{2}} = \frac{G ρ \frac{4}{3} π r^{3}}{r^{2}} = \frac{4}{3} G π ρ r$
Given $E_{G}$ is constant,
$\Rightarrow ρ \times r = c o n s t a n t \Rightarrow ρ \propto \frac{1}{r}$

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If the intensity of gravitational field at all places inside earth is presumed to be constant, then the relation between the density of earth (ρ) and distance (r) from the centre of the earth will be :

The correct option is C ρ∝1rGravitational field intensity EG is given byEG=GMr2=Gρ43πr3r2=43GπρrGiven EG is constant,⇒ρ×r=constant⇒ρ∝1r

If the intensity of gravitational field at all places inside earth is presumed to be constant, then the relation between the density of earth $(ρ)$ and distance $(r)$ from the centre of the earth will be :

The correct option is C $ρ \propto \frac{1}{r}$
Gravitational field intensity $E_{G}$ is given by
$E_{G} = \frac{G M}{r^{2}} = \frac{G ρ \frac{4}{3} π r^{3}}{r^{2}} = \frac{4}{3} G π ρ r$
Given $E_{G}$ is constant,
$\Rightarrow ρ \times r = c o n s t a n t \Rightarrow ρ \propto \frac{1}{r}$