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`        A non uniform rod AB has a mass M and length 2L. The mass per unit length of the rod is mx at a point of the rod distant x from A. Find moment of inertia of this rod about an axis perpendicular to the rod(a) through A (b) through the mid point of AB.`
7 years ago

510 Points
```										let the rod is placed along x axis and  its end A is at origin........
consider a small element of thickness dx at a distance x from end A..
mass of element is (mass per unit length)(length of this element)
dm=mxdx........1
moment of inertia of this element about the axis passing through its  end A and perpendicular to rod is dmx^2
dI=dmx^2
=mx^3dx
total moment of inertia is integral of dI limit from 0 to 2L
I=integral(mx^3dx)    lim 0 to 2L
=m (2L)^4 /4
I =4mL^2

```
7 years ago
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