Question

At what depth below the earth's surface
the value of g will be 25% of its volume
earth surface ? Assume the earth as a homogeneous sphere of radius R.
​

Answer 1

Answer:

At a height h above the earth's surface, we have

g

′

=g(

R+h

R

)

2

⇒

4

g

=g(

R+h

R

)

2

⇒

R+h

R

=

2

1

⇒h=R=6400km

b. At a depth h below the earth's surface, we have

g

′

=g(1−

R

h

)⇒

g

g

′

=1−

6400

4

g

g−g

′

=

6400

4

⇒

g

Δg

=

16

!

∴% age=

g

Δg

×100=

16

1

% increase