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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Badiuddin

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.