Find the center of mass the rod in the figure if λ (the mass per unit lenght) varies with $x$ according to $\lambda=dm/dx=\beta x^2$, where $\beta$ is a constant.
Sorry for quality of picture. I am waiting for your help.
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3$\begingroup$ When in doubt, choose C. More seriously, you'll need to show effort and precisely where you are getting stuck. If your issue is conceptual, then we might be able to help. $\endgroup$– BMSCommented Dec 16, 2014 at 23:34
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1 Answer
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The center of mass of an object is the point where the first moment of mass is zero. Put differently, when you support the object at that point, it will be balanced.
Assume that point is $x_0$, then
$$\int_0^\ell (x-x_0) \lambda(x) dx = 0$$
Substitute $\lambda$ and some simple manipulation will give you an expression for $x_0$.
Let us know how far you get with that.
