1.

Show that the centre of mass of a uniform rod of mass M and length L lies at the middle point of the rod.

Answer»

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 l = M/L

Hence, dm, (the mass of the element dx situated at x = x is) = l dxThe coordinates of the element dx are (x, 0, 0). Therefore, x-coordinate of COM of the rod will beX=0The y-coordinate of COM isy=0 Similarly, zCOM= 0

i.e., the coordinates of COM of the rod are ( 0, 0), i.e., it lies at the centre of the rod.



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