Physics, 28.08.2019 10:10 joelpimentel

Why gravitational force at the center og earth is zero

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Answer from: kyleescott9525

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$\huge{\green{\tt{\underline{\underline{QUESTION:-}}}}}$

Why value of 'g' is zero at center of Earth?

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$\huge{\red{\tt{\underline{\underline{EXPLANATION:-}}}}}$

When we move towards centre of earth, the mass is equally distributed in all directions.

The mass beneath you = Mass in front of you = Mass behind you

Thus, all the gravitational forces applied cancel each other and acceleration due to gravity (g) at centre of earth on centre of earth becomes zero (0).

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$\huge{\green{\tt{\underline{\underline{PROOF:-}}}}}$

The general equation of acceleration due to gravity is;-

g = $\frac{GM}{r^2}$

Assuming earth to be a perfect sphere and considering its uniform density.

We make the following adjustments in the following equation.

g = $\frac{GM}{r^2}$

Multiplying and dividing RHS by volume 'V'.

g = $\frac{GM}{V} × V × \frac{1}{r^2}$

We know that;-

$\frac{M}{V}$ = Density, ρ

Therefore,

g = $\frac{ρGV}{r^2}$

For sphere;-

V = $\frac{4}{3}$ π $r^{3}$

This makes

g = $\frac{4}{3}$ π $r^{3}$ × $\frac{ρG}{r^2}$

g = $\frac{4πρG}{3}$

So, at center of Earth

since, r = 0

so, g = 0.

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Answer from: Quest

with the invention of the automobile, the woman of the house could drive to the store and get groceries. women were also free to socialize more. during world war ii women were allowed to work in factories to the war effort and could drive to work or ride mass transit buses to their jobs.

Answer from: Quest

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.

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