Question

calculate the value of g at a height of 3600 km above the surface of the earth

Answer 1

The formula for value of gravity at any height his given by:

gh = g(1 -h/R)

where R

is radius of earth and it's value is equal to 6400km

Now,

gh = g(1 - 3600/6400)

gh = g(6400 - 3600) / 6400

gh = g(2800) / 6400

gh = 9.8 × 2800/6400

gh = 4.01 m/s

Answer 2

Given:

The height of a particle is a height of 3600km from the surface of the earth.

To find:

The value of g at that point.

Solution:

Let the gravity at that point be$g_{h}$.  

$g_{h} = \frac{g}{1+\frac{h^2}{r^2} }$

Where,

• g = gravity of earth (g = 10m s^-2)

• h = height of the particle from the surface of the earth

• r = radius of Earth = 6400 km

Substitute the values in the given formula,

 

=>$g_{h}$ = $\frac{g}{1+\frac{(3600)^2}{(6400)^2} }$

= > $g_{h}$ = $\frac{g}{(1+\frac{9}{16} )^2}$,

= > $g_{h}$ =$\frac{(16^2)*g}{(25)^2}$ .

 

Substitute the value of g as 10ms^-2,

= > gh = (256 x 10)/625,

= > gh = 4.096 ms^-2.

Therefore, the value of g at a height of 3600km from the surface of the earth is 4.096 ms^-2.