Question

Obtain the formula for the gravitational acceleration at a depth d from the earth's surface.

Answer 1

Answer:

The gravitational acceleration at depth d from the earth's surface$\ =\ \dfrac{G\times\ M}{(r-d)^{2}}$

Explanation:

Let's consider that

the radius of the earth = r

Mass of the earth= M

and the gravitational constant = G

as given depth from the earth's surface= d

Consider all the given quantity is in S.i units.

As the acceleration due to gravity at earth's surfce$\ =\ \dfrac{G\times\ M}{r^{2}}$

Hence, the gravitational acceleration at depth d from the earth's surface$\ =\ \dfrac{G\times\ M}{(r-d)^{2}}$