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Find position of center of mass of 1m long non uniform rod that extends on x...

Find position of center of mass of 1m long non uniform rod that extends on x axis and linear density lamda = x^2.

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Answer #1

Linear mass density of the rod is

Assuming the left end of the rod is at x1=0, then right end of the rod will be at x2=1m because the length of the rod is 1m.

Total mass of the rod is

The center of mass is given by

Using (1)

If the left end is at x1=0, and right end at x2=1m we get

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