Find a mass density function so that , the center of mass of a rod of length , is at a distance from one end.

Let

Then we compute the center of mass of the rod,

Thus, the center of mass is a distance from one end.

Skip to content
#
Stumbling Robot

A Fraction of a Dot
#
Find a mass density function so the center of mass is at L/4

###
3 comments

### Point out an error, ask a question, offer an alternative solution (to use Latex type [latexpage] at the top of your comment):

Find a mass density function so that , the center of mass of a rod of length , is at a distance from one end.

Let

Then we compute the center of mass of the rod,

Thus, the center of mass is a distance from one end.

x^(-2/3) also works, doesn’t it? for the other side

How did you know that the density should be x squared.. I mean is there a method for that or you have guessed it?

L/4 from the end which mean 3L/4 from the start. then. 3L/4 = 3x^4/4x^3 from 0 to L=> int(x^3)/int(x^2)=int(x*p(x))/int(p(x)). =>p(x)=x^2.

hope it helps