Question

The decrease in the value of g on going to a height above the earth's surface will be

Answer 1

For rising a height of h

g' = 1-(h/g)

Answer 2

To find :

The decrease in the value of g on going to a height above the earth's surface.

Solution :

We know , acceleration due to gravity at earth's surface is given by :

$g=\dfrac{GM}{{R_e}^2}$

Now , at height h , let acceleration due to gravity be $g'$ .

Force due to gravity is :

$F=\dfrac{GmM}{(R_e+h)^2}\\\\mg'=\dfrac{GmM}{(R_e+h)^2}\\\\g'=\dfrac{G M}{(R_e+h)^2}$

Taking , ${R_e}^2$ common from denominator .

We get :

$g'=\dfrac{GM}{R_e^2}\dfrac{1}{(1+\dfrac{h}{R_e})^2}$

Therefore ,

$g'=\dfrac{g}{(1+\dfrac{h}{R_e})^2}$

Hence , this is the required solution .

Learn More :

Gravitation

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