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A non-uniform rod AB has mass M and length 2L, The mass per unit the length of the rod is mx at a point of the rod distant x from A. find the moment of inertia of the rod about an axis passing through A.

A non-uniform rod AB has mass M and length 2L, The mass per unit the length of the rod is mx at a point of the rod distant x from A. find the moment of inertia of the rod about an axis passing through A.
 

Grade:12th pass

1 Answers

Aakash
110 Points
9 years ago
Consider a small element dx. x distance away from point A.
mass of small element = (Mx)*dx
Moment of inertia, dI = (Mx)*dx*x2
Integrating both sides
I = M( ∫ x3 dx)
limit 0 to 2L
I = M[x4/4]
Putting limits
I = M[(16L4/4)-0]
I = 16ML4/4 = 4ML4

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