- #1
1v1Dota2RightMeow
- 76
- 7
Homework Statement
A solid sphere of density ##ρ## and radius ##R## is centered at the origin. It has a spherical cavity in it that is of radius ##R/4## and which is centered at ##(R/2, 0, 0)##, i.e. a small sphere of material has been removed from the large sphere. What is the the center of mass ##R_{cm} = (x_{cm}, y_{cm}, z_{cm})## of the large sphere, including the cavity?
Homework Equations
##R=1/M \int \rho r dV##, where ##dV=dxdydz## and ##\rho = dm/dV## and ##M=## total mass
The Attempt at a Solution
##R=(1/M) \int r dm = (1/M) \int \rho r dV##
##M##= total mass = ##\rho V = \rho(V_{total} - V_{cavity})##
##R=(1/(\rho(V_{total} - V_{cavity})) \int \rho r dV##
Here, I see that the ##\rho##'s cancel. But now I'm stuck wondering what ##r## is.