Question

13. At what altitude in metre will the acceleration due to gravity be 25% of that at earth’s

surface (Given, Radius of earth = R metre)

a. 1/4R

b. R

c. 3/8R

d. R/2​

Answer 1

Answer:

b is the correct option

Force on the body placed on Earth's surface is

F=

R

2

GMm

But, F=mg hence,

mg=

R

2

GMm

where, variables have their usual meanings.

gR

2

=GM

Now, force on the body at geo-potential height say h (altitude) where the acceleration due to gravity is 25% of that at the earth's surface i.e.

100

25g

=

4

g

Hence, we can write

4

g

=

(R+h)

2

GM

4

g

=

(R+h)

2

gR

2

(R+h)

2

=4R

2

Taking roots for both sides we get

R+h=2R

h=R