Question

Calculate the acceleration due to gravity inside earth as a function of the radial distance r from the planet's center. (hint: imagine that a mine shaft has been drilled from the surface to earth's center and an object of mass m has been dropped down the shaft to some radial position rr from the center? d

Answer 1

The acceleration due to gravity inside earth is r G Me / Re³

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Further explanation

Newton's gravitational law states that the force of attraction between two objects can be formulated as follows :

$\large {\boxed {F = G \frac{m_1 ~ m_2}{R^2}} }$

F = Gravitational Force ( Newton )

G = Gravitational Constant ( 6.67 × 10⁻¹¹ Nm² / kg² )

m = Object's Mass ( kg )

R = Distance Between Objects ( m )

Let us now tackle the problem !

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Given:

radius of Earth = Re

distance of object from centre of the Earth = r

mass of object = m

mass of the Earth = Me

Asked:

acceleration due to gravity inside Earth = g = ?

Solution:

$g = G \frac{M}{r^2}$

$g = G \frac{ \frac{r^3}{(R_E)^3} M_E}{r^2}$

$g = G \frac{ r M_E}{(R_E)^3}$

$\boxed{g = r G \frac{ M_E}{(R_E)^3}}$

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Conclusion :

The acceleration due to gravity inside earth is r G Me / Re³

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Gravitational Fields

Answer 2

An estimated value for gravity at a distance r from the middle of the Earth can be gotten by supposing that the Earth's density is spherically symmetric. The gravity hinge on only on the mass inside the sphere of radius r. All the assistances from outside cancel out as a fall out of the inverse-square law of gravitation. Another result is that the gravity is the same as if all the mass were concentrated at the midpoint. Therefore, the gravitational acceleration at this radius is 
g(r) = GM(r) / r² 
M(r) = mass enclosed by radius r. 
If the Earth had a continual density ρ, the mass would be M(r) = (4/3)πρr³ and the dependence of gravity on distance would be 
g(r) = (4/3)πGρr 
G = 6.674e-11 m³/kgs²