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rajan jha Grade: 12
        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.
6 years ago

Answers : (1)

vikas askiitian expert
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


 

6 years ago
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