Question

a meteor of mass 200 kg is at a height of 12800 km from the centre of the earth having mass 6*10^24 kg and radius 6400 km . Find the weight of the meteor at the height.​

Answer 1

Given that,

Gravitational potential U=−5.12×10

7

J\kg

Acceleration due to gravity g=6.4m/s

2

Let r be the distance of the given point from the center of the earth.

We know that,

Gravitational potential U=−5.12×10

7

=

r

−Gm

....(I)

Acceleration due to gravity g=6.4=

r

2

Gm

....(II)

Now, dividing equation (I) by equation (II)

Gm×r

Gm×r

2

=

6.4

5.12×10

7

r=0.8×10

7

m

r=8000km

Now, the height of the point from earth’s surface

h=r−R

h=8000−6400

h=1600km

Hence, the height is 1600 km