# Center of mass of a cone

## Homework Statement

Calculate the X_com of the cone of mass M in terms of quantities given in the picture. The density of the cone is uniform.

See the attachments for the picture.

## The Attempt at a Solution

When I did it I got

X_com = (3L)/2

and I am unsure if this is correct or not. The infinitely small sections are circular disks of area pi R^2 were r is the radius of the infinitely small disk and a volume just an infinitely small width dx times the area. therefore the density

rho = dm/dV = dm/(pi R^2 dx)

I sort of got confused when I did because the radius changes with respect to x and during the middle of the test I sort of rushed this problem and thought that it just canceled out in the end but believe I may be wrong

#### Attachments

• Untitled.jpg
13.1 KB · Views: 374
• Capture.PNG
119.9 KB · Views: 414

SteamKing
Staff Emeritus
Homework Helper
You have shown that the center of mass of the cone in the x-direction lies outside of the cone. Your answer is not correct.

Yes, the radius changes with respect to x, but it does so in a predictable manner.

Care to reformulate your solution to the c.o.m.? Concentrate on writing the moment equation using the origin as the reference point.

what is the moment equation?

SteamKing
Staff Emeritus
Homework Helper
It's an essential component in your c.o.m. calculation.

d(moment)/dx = x * dm

Im not exactly sure what is meant by moment in your equation. Can someone tell me. I recalculated it except this time I got 3/4 R. I believe the answer is 3/4 L though. I'm not exactly sure what I did wrong. Thanks for any help.

sorry that a four in the denominator magically disappeared from my work towards the end and magically reappeared. I just realized this. Everything else is correct though I believe, except some reason I got 3/4 R instead of 3/4 L

#### Attachments

• Untitled.jpg
34.8 KB · Views: 416
Last edited: