"FIND" MOI

for a rectangle let the length be a and breadth be b

then M.I along the length will be Ma²/12

and along the breadth will Mb²/12

then according to perpendicular axis theorem

I_z=I_x+I^y

since length and breadth are perpendicular

I= ma²/12+mb²12

hence I =ma²+b²/12

rectangle:

consider the figure.. if u take an element..as shown..
dm = (M/ab)*bdx =Mdx/a
dI = dm.x² = Mx²dx/a
So, I = ∫Mx²dx/a (from -a/2 to a/2)
= M[x³/3]/a

evalutaing limits it is I = Ma²/12

If u wud have taken parallel to side a then I = Mb²/12

And abt COM and perpendicular to plane = M(a²+b²)/12

thnx asis n amit [1]

C this :

the ans here is C

H = Iω
==> H = M(2d)²/12ω
==> ω = 3H/Md²

The axis is in the plane of the plate and parallel to L so its MOI = M.(2d)²/12 .. see in the derivation abv... the MOI of rectangle parallel to a = mb²/12 ... thats y here the MOI will be as taken

diagonal of cuboid is it in the ques??
not of cube......
anyways lets find of cuboid and then from its expression we shall know that of cube