# 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.

148 Points
14 years ago

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 = o2Ldm * x2

=o2Lm * x3 dx

=4mL4

and we know M =o2Ldm

= o2Lmxdx

=2mL2

so moment of inerta  I =2ML2

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Arijit Banerjee
18 Points
11 years ago

1.  Particles of masses 1g,2g,3g,....,100g are kept at the marks 1cm,2cm,3cm,...,100cm respectively on a metre scale .Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

2.