IIT JEE , AIEEE Forum - Physics , Mechanics

nikhiljee2007

Take a rectangular element:-
1. width : dx
2. length : a
3. at a perpendicular distance x from centre.
mass/area = y = M/a*a

moment of inertia of this element : (dm)a*a/12[about its centre]
moment of inertia of this element : (dm)a*a/12+(dm)*x*x
[about centre of plate]

dm=(M/a*a)*(a*dx)= (M/a)dx
now integrate:-
Inertia =M/a integral[(a*a/12)+x*x] dx { limit -a/2 to a/2}
= M*a*a/6

Using Perpendicular axis theorem
inertia along first dig. + inertia along second dig. = inertia along centre

Inertia along digonal = 0.5 * inertia along centre
= M*a*a/12

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