Question

a man weighs 600 N at earth's surface at what height above the surface of Earth will he weigh 300 Newton take radius of the earth to be 6400 km please answer this question

Answer 1

this may help u.......

Answer 2

Answer:The height above the surface of the earth is 2649.6 km.

Explanation:

Given that,

Radius of earth R = 6400 km

Weight of the man at earth mg = 600N

$g = \dfrac{600}{m}$

Weight of the man at height above the earth's surface mg'=300N

$g'=\dfrac{300}{m}$

We know that,

The gravity at the surface of the earth is

$g = \dfrac{GM}{R^2}$.....(I)

The gravity at the height above the earth's surface

$g' = \dfrac{GM}{(R+h)^2}$.....(II)

Divided equation (I) by equation (II)

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

Put the value of g and g' in equation (III)

$\dfrac{600}{300}=\dfrac{(R+h)^2}{R^2}$

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

$\dfrac{(R+h)}{R}=\sqrt{2}$

$h = R(\sqrt{2}-1)$

$h = 6400\times1.414-6400$

$h = 2649.6\ km$

Hence, The height above the surface of the earth is 2649.6 km.