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A non-uniform rod AB has a mass M and length 2l.The mass per unit lengthof the rod is mx at a point of the rod distant x from A. find the moment of inertia of this rod about an axis, a)through A,b) through the mid point of AB. Ans) let a element of length dx at adistance x from the point A of the rod.mass of this element will be dm = mxdxso moment of inertia of this element about point A is dI = dm * x2for moment of inertia of whole rod perform intigrationI= ∫dI = o∫2Ldm * x2 =o∫2Lm * x3 dx =4mL4and we know M =o∫2Ldm = o∫2Lmxdx =2mL2so moment of inerta I =2ML2
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