Simple Density Law: Prove Central Density 4x Mean

In summary, the conversation discusses how to show that a spherical body with a specific density function has a central density that is 4 times larger than its mean density. The conversation progresses from the initial problem statement to the student seeking help and eventually figuring out the solution with the help of hints.
  • #1
seto6
251
0

Homework Statement


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).


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!
 
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  • #2
help?please
 
  • #3
can some1 tell me how to approch this problem ...
 
  • #4
If you know the density of the object at each point, do you know how to compute its mass?
 
  • #5
nop.
 
  • #6
seto6 said:
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?
 
  • #7
sure
 
  • #8
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
 
  • #9
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
let me give it ago and get back
 
  • #11
OMG! thank you soo much... i figured it out! and showed it too..RESPECT TO YOU :smile:
 
Last edited:

Related to Simple Density Law: Prove Central Density 4x Mean

1. What is the Simple Density Law?

The Simple Density Law is a scientific principle that states that the density of a substance is equal to its mass divided by its volume. This law applies to all types of matter, including solids, liquids, and gases.

2. How is the Simple Density Law calculated?

The Simple Density Law is calculated by dividing the mass of an object by its volume. This can be expressed mathematically as D = m/v, where D is density, m is mass, and v is volume.

3. What is the significance of the Central Density 4x Mean in the Simple Density Law?

The Central Density 4x Mean is a specific value that is used in the Simple Density Law to represent the average density of a substance. It is calculated by multiplying the central density of a substance by four.

4. How can the Simple Density Law be applied in real life?

The Simple Density Law has many practical applications in fields such as chemistry, physics, and engineering. It is used to determine the density of various materials, which can be useful in designing and manufacturing products, as well as in conducting scientific research.

5. Can you provide an example of how to use the Simple Density Law?

Sure, let's say we have a cube of gold with a mass of 50 grams and a volume of 10 cm3. To calculate the density, we would divide the mass (50g) by the volume (10 cm3). This gives us a density of 5 g/cm3. Using the Central Density 4x Mean, we can say that the average density of gold is 20 g/cm3 (5 g/cm3 x 4).

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