Find out the location of centre of mass of a uniform rod.

1.	Find out the location of centre of mass of a uniform rod.
Answer» Solution :Suppose a rod of mass M and length L is lying along the X-axis with its ONE END at x=0 and the other at x = L Mass per unit length of the rod =`M/L` Hence, mass of the element PQ of length dx situated at a DISTANCE V from the origin is DM =`M/L` dx The coordinates of the element PQ are (x, 0,0). Therefore, x -coordinate of CM of the rod will be: `x_(CM) = (int_(0)^(L)xdm)/(intdm) =(int_(0)^(L)(x)(M/Ldx))/M = I/L int_(0)^(L) xdx = L/2, y_(cm) =(int ydm)/(int dm)=0`

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