Question

a man weight 600 Newton at the surface of the earth at what height above the surface of the earth will he weigh 300 Newton take the radius of the earth to be 6400. km

Answer 1

Answer:

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

Answer 2

Given,

Weight on surface of Earth = 600 N

Weight above surface of Earth = 300 N

Radius of Earth, R = 6400 km

To find,

Height, h above the surface of the earth where man weighs 300 N

Solution,

Weight on surface of Earth = 600 N

Mg = 600 N

$g = \frac{600}{M}$                                                                                           (I)

Weight above surface of the earth = 300 N

Mg' = 300 N

$g' = \frac{300}{M}$                                                                                           (II)

Gravitational acceleration is given as,

$g = \frac{GM}{R^{2} }$                                                                                           (III)

Substituting (I) in (III)

$g = \frac{GM}{R^{2} } = \frac{600}{M}$                                                                                   (IV)

Now substituting (II) in (III)

$g' = \frac{GM}{(R+h)^{2} } = \frac{300}{M}$                                                                                    (V)

Here h is the height above the surface of the Earth.

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

Using (IV) and (V) the equation can be written as,

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

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

$\sqrt{2} = \frac{R + h}{R}$

$\sqrt{2} R = R + h$

$\sqrt{2} R - R = h$

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

The radius, R, of the earth is 6400 km

∴ $h = 6400 (1 - 1.414)$

h = 2649.6 km

The height at which the man will weigh 300 N above the surface of the Earth is 2649.6 km.