# Question #6ab42

##### 2 Answers

I found

#### Explanation:

Consider the following:

The Law of Gravitation gives you:

If: radius Earth

on the surface you have:

In your case you have:

* _ * _ _(1)

The problem is

If density of Earth is

So substituting in (1)

Here's how you can solve this one without knowing Earth's radius.

#### Explanation:

The idea of this problem is that you need to use the fact that the *gravitational acceleration*, **decreases** as you move *away* from the surface and as you move *towards* the center of the planet.

At the surface, the gravitational acceleration is given by this equation

At a distance equal to **above the surface**, the gravitational acceleration will be

The trick here is to divide this value by the value of

Now, when **much smaller** than

Use binomial expansion to write this as

Since

The gravitational acceleration at a height

At a distance **below the surface**, the gravitational acceleration will be

*attracts* the body.

SInce you're below the surface, **not all the mass** of the Earth will contribute to the value of *smaller radius*, i.e.

Assuming that Earth's density is constant, you can write

This means that

Once again, divide this by the value of

The gravitational acceleration at a distance

Now all you have to do is set these two equations equal to each other and solve for

This is equivalent to

In your case, **10 km**, therefore