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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.
Dear niharika
let a element of length dx at adistance x from the point A of the rod.
mass of this element will be dm = mxdx
so moment of inertia of this element about point A is
dI = dm * x2
for moment of inertia of whole rod perform intigration
I= ∫dI = o∫2Ldm * x2
=o∫2Lm * x3 dx
=4mL4
and we know M =o∫2Ldm
= o∫2Lmxdx
=2mL2
so moment of inerta I =2ML2
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2.
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