Question

Explain how the value of 'g' changes with altitude

Answer 1

Let A be the point on the surface of the earth and B be the point at an altitude h. Let M be the mass of the earth and R be the radius of the earth. ... the value of acceleration due to gravity decreases with increase in height above the surface of the earth.

Answer 2

To Find :

How the value of 'g' changes with altitude .

Solution :

Let , the height of object from the surface of earth is , h .

So , the force of attraction is given by :

$F=\dfrac{GM}{(R+h)^2}$

Also , force is given by :

$F=Mg_h$

Here , $g_h$ is acceleration due to gravity at height h .

So ,

$Mg_h=\dfrac{GM}{(R+h)^2}\\\\g_h=\dfrac{GM}{R^2}\times \dfrac{1}{(1+\dfrac{h^2}{R^2})}$   .......1

Here , $\dfrac{GM}{R^2}=g$

Putting value of $\dfrac{GM}{R^2}$  in 1 , we get :

$g_h= \dfrac{g}{(1+\dfrac{h^2}{R^2})}$

Therefore , value of g changes at  $g_h= \dfrac{g}{(1+\dfrac{h^2}{R^2})}$ .

Hence , this is the required solution .