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3 years ago

Why gravitational force at the center og earth is zero

Physics

2 answers:

KengaRu [80]3 years ago

8 0

F = G Mm/r²
mg = G Mm/r²
g = GM/r²
At centre of earth, r=0
g = GM/0
g =0

Anon25 [30]3 years ago

4 0

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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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For this case, let's assume that the pot spends exactly half of its time going up, and half going down, i.e. it is visible upward for 0.245 s and downward for 0.245 s. Let us take the bottom of the window to be zero on a vertical axis pointing upward. All calculations will be made in reference to this coordinate system. 

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s=(v)(t)+(1/2)(a)(t^2)

to solve for v, the initial velocity of the pot as it enters the cat's view through the window. Substituting and solving (note that gravitational acceleration is negative since this is opposite our coordinate orientation):

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v=8.549m/s

Now we know the initial velocity of the pot right when it enters the view of the window. We know that at the apex of its flight, the pot's velocity will be v=0, and using this piece of information we can use the kinematic equation:

(v final)=(v initial)+(a)(t)

to solve for the time it will take for the pot to reach the apex of its flight. Because (v final)=0, this equation will look like

0=(v)+(a)(t)

Substituting and solving for t:

0=(8.549m/s)+(-9.81m/s^2)(t)

t=0.8714s

Using this information and the kinematic equation we can find the total height of the pot’s flight:

s=(v)(t)+(1/2)(a)(t^2)

s=8.549m/s (0.8714s)-0.5(9.81m/s^2)(0.8714s)^2

s=3.725m

This distance is measured from the bottom of the window, and so we will need to subtract 1.80m from it to find the distance from the top of the window:

3.725m – 1.8m=1.925m

Answer:

1.925m

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Answer:

Explanation:

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then dog travels 8.2 m , 23.1 degree north of east

Displacement D₂ = 8.2 cos23.1 i + 8.2 sin23 j

D₂ = 8.2 cos23.1 i + 8.2 sin23.1 j

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Third displacement

D₃ = - 15i

Total displacement = D₁ + D₂ + D₃

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= 7.46 m

b ) Direction of displacement

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Korolek [52]

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