# Simple density law

1. Sep 26, 2010

### seto6

1. The problem statement, all variables and given/known data
Show that a spherical body with density
p (r) =Pc(1−x)
where x = r/R and R its radius, has a central density pc that is 4 times larger than the mean density (< p > =mass/volume).

2. Relevant equations

not sure

3. The attempt at a solution

im not sure how to start this problem... can someone give me a hit on doing this question. please!

2. Sep 26, 2010

### seto6

help?plz

3. Sep 26, 2010

### seto6

can some1 tell me how to approch this problem ...

4. Sep 26, 2010

### Dick

If you know the density of the object at each point, do you know how to compute its mass?

5. Sep 26, 2010

### seto6

nop.

6. Sep 26, 2010

### Dick

Not knowing any relation between the density function and the mass might be the root of your problem. Could you try and look something up?

7. Sep 26, 2010

### seto6

sure

8. Sep 26, 2010

### seto6

i know that p=m/v and v=(4/3) pi R^2

umm could you post some links b/c im googleing it not much tho

9. Sep 26, 2010

### Dick

It might be better to check your notes or the textbook. In general you find the mass by doing the triple integral of density*dV. I'll give you a hint that if the density is spherically symmetric then the mass is the integral from 0 to R of density*4*pi*r^2*dr. Does that sound familiar? If you can show that form follows from the density*dV formula by using spherical coordinates, I'll give you extra virtual points.

10. Sep 26, 2010

### seto6

let me give it ago and get back

11. Sep 26, 2010

### seto6

OMG!!!:surprised thank you soo much... i figured it out! and showed it too..

RESPECT TO YOU

Last edited: Sep 27, 2010