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bharath devasani Grade: 12
        

A non uniform rod AB  of mass M and length 2l. the mass per unit lenght of the rod is mx.At  a point of the rod distance x from A.


Find the moment of inertia of this rod.About an axis perpendicular to the rod through A

6 years ago

Answers : (2)

SAGAR SINGH - IIT DELHI
879 Points
										

Dear bharath,


This is a very simple problem of Integration.


Length of the rod is 2l. Let 0 be its centre. Take any small element dx on the rod.


Then Moment of inertia Integral mx2dx and integrate it from -l to +l.


So we get 2ml3/3 as the required moment of inertia...


 


 


Sagar Singh


B.Tech, Chemical Engg


IIT Delhi

6 years ago
vikas askiitian expert
510 Points
										

let the rod of length 2L is placed in +ve x axis with its end A is at origin.....


consider a small element dx at a distance x from origen.......


mass of that element is dm=(linear mass density).dx


                                      dm =mxdx


now moment of inertial of this small element about end A is


          dI=dmx^2


             =(mxdx)x^2


           dI  =mx^3dx


now integrating this expression limit from 0 to 2L


          I=16mL^4/4


           I=4mL^4 units


 approve my ans if u like


 

6 years ago
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