Question

1). What is the gravitational potential due to
the Earth at a point which is at a height
of 2R above the surface of the Earth,
Mass of the Earth is 6x1024 kg, radius of
the Earth = 6400 km and G = 6,67x10-
Nm²kg 2.​

Answer 1

Given that,

Gravitational potential

U=

−5.12×

10 7

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

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