Question

If g, is the acceleration due gravity at a depth d' and g, the acceleration due to gravity at a height h from the surface of the earth (if h=d)

a) gd > gh
b) gd < gh
c) gd = gh
d) depends on h​

Answer 1

Explanation:

Let the radius of the earth be R and acceleration due to gravity at earth surface be g.

Acceleration due to gravity at height h above the earth surface, g

h

=g(1−

R

2h

)

Acceleration due to gravity at depth d below the earth surface, g

d

=g(1−

R

d

)

Now for g

h

=g

d

we get, g(1−

R

2h

) =g(1−

R

d

)

⇒ 1−

R

2h

=1−

R

d

⇒ d=2h