Question

the moment of inertia of a door of mass m , length 2l and width l about its longer side is :

ans : ml square/3

Answer 1

element mass dm'= ρdx  where ρ= linear density
therefore, m'=ρx
  =mlx  where m is the mass of the door
now moment of inertia is given by,
I=m'r2 =(mxl)x2 
this is the moment of inertia of a rigid body( uniform rod) about the axis which is given by,
I=ml212
similarly, the moment of inertia of the rectangular door about a line parallel to its length thought the centre is given by
I=m(2l)212=ml23

Answer 2

Answer:

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