Question

Calculate the value of ‘g’ at a height of 12800 km from the centre of the earth (radius of earth is 6400 km). Draw its interpretation.

Answer 1

g means acceleretion due to gravity.

therfore, g=GM/R^2

here, height is given 12800km
(R+H) must use in the above formula

g=GM/(R+H)^2
we have to take distance and radius in meters

therefore, R=6400000
and, H=12800000

g=6.67*10^-11 * 6*10^24/(6400000+12800000)^2

g=40.02*10^13/(19.2*10^6)^2

by solving above equation, we get,

g=1.09m/s^2
I HOPE YOU WILL SATISFIED WITH THIS ANSWER

Answer 2

The value of acceleration due to gravity 'g' at a height of 12800 km from the centre of the Earth is equal to 2.45 ms⁻².

Given:

The height from the centre of the Earth = 12800 km

The radius of the Earth = 6400 km

To Find:

The value of g at a height of 12800 km from the centre of the earth.

Solution:

→ The value of acceleration due to gravity g at a height 'h' above the Earth's surface is given as:

                                        $\fbox{\boldsymbol{g'=\frac{g}{(1+\frac{h}{R})^{2} } }}$

• where g' is the acceleration due to gravity at a height 'h' above the Earth's surface.
• where 'R' is the radius of the Earth.

→ In the given question:

The acceleration due to gravity at the Earth's surface (g) = 9.8 ms⁻²

The radius of the Earth (R) = 6400 km

The height from the centre of the Earth = 12800 km

∴ The height from the surface of the Earth (h) = 12800 - 6400 = 6400 km

Let g' be the acceleration due to gravity at a height 'h' above the Earth's surface.

                                           $\fbox{\boldsymbol{g'=\frac{g}{(1+\frac{h}{R})^{2} } }}$

                                         $\boldsymbol{\because g'=\frac{g}{[1+\frac{h}{R} ]^{2} } }\\\\\boldsymbol{\therefore g'=\frac{9.8}{[1+\frac{(6400)}{(6400)} ]^{2} } }\\\\\boldsymbol{\therefore g'=\frac{9.8}{[1+1 ]^{2} } }\\\\\boldsymbol{\therefore g'=\frac{9.8}{4} }\\\\\boldsymbol{\therefore g'=2.45\:ms^{-2} }$

→ The value of g' comes out to be equal to 2.45 ms⁻².

Therefore the value of acceleration due to gravity 'g' at a height of 12800 km from the centre of the Earth is equal to 2.45 ms⁻².

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