Simple Density Law: Prove Central Density 4x Mean

[seto6]

Homework Statement

Show that a spherical body with density
p (r) =P_c(1−x)
where x = r/R and R its radius, has a central density p_c that is 4 times larger than the mean density (< p > =mass/volume).

Homework Equations

not sure

The Attempt at a Solution

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

 

[seto6]

help?please

 

[seto6]

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

 

[Dick]

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

 

[seto6]

nop.

 

[Dick]

nop.

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?

 

[seto6]

sure

 

[seto6]

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

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

 

[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.

 

[seto6]

let me give it ago and get back

 

[seto6]

OMG! thank you soo much... i figured it out! and showed it too..RESPECT TO YOU