# Gravitation: Force inside a sphere

1. Jan 14, 2004

### Rockdog

A solid sphere has a uniform density, a mass of 17 kg and a radius of 2.2 m.
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a) What is the force due to gravity from the sphere on a very small object of mass 21 grams located 1.1 m from its center?

b) What is the force due to gravity from the sphere on a very small object of mass 21 grams located 3.3 m from its center?

How do I start this problem? I know that F=G*m1*m2/R
and Mass inside a shell= density*(4/3)pi*r^3, but it just confuses me more.

2. Jan 14, 2004

### NateTG

Can you determine the net force of gravity on an object inside a spherical shell, and outside a spherical shell. You might find it in your textbook. It will make your life a lot easier.

3. Jan 15, 2004

### rgrig

The quick way of solving it is to use the fact that if you have a sphere of radius r1 and an object inside at distance r2 (r2<r1) from the center of the sphere then only matter at distance x<r2 from the center would give a net gravitational effect. All other effects cancel each other because of the symmetry (I'm assuming, of course, that everything stands still).

The good way to do it is to proove the above "fact", for example by adding up all contributions (integral).

regards,
http://www.geocities.com/_rgrig
http://rgrig.blogspot.com/

4. Jan 15, 2004

### HallsofIvy

Staff Emeritus
One can show that the net gravitational force on an object inside a hollow sphere is 0. That's because the pull due to a small section of mass is exactly offset by the pull of the mass opposite the first section.

One can also show, by symmetry, that the gravitational force, due to a spherical mass, on an object outside the sphere is exactly the same as if the mass were concentrated at the center of the sphere.

To answer the first question, use the density to calculate the mass of the portion of the sphere inside radius 1.1 m and treat it as a mass concentrated at the center.

To answer the second, treat the entire 17 kg as if it were concentrated at the center.

5. Jan 15, 2004

### Rockdog

Sorry, can you explain something first.
First part, I figured out the density value to calculate the mass of the portion of the sphere inside radius 1.1 m. Now you say treat it as a concentrated mass at the center of the sphere. Ok, but I mean, what do I do with it in terms of calculation?

2) Can you explain why its the entire 17kg?