Question

Moment of inertia of rectangular wire frame about its diagonal is

Answer 1

Hello dear,

● Answer-
Id = m(l^2+b^2)/24

● Explanation-
Let's consider,
Id = M.I. about diagonal
Il = M.I. about length = ml^2/12
Ib = M.I. about breadth = mb^2/12

By perpendicular axis theorem-
Il + Ib = 2Id
Id = (Il + Ib) / 2
Id = (ml^2/12 + mb^2/12) / 2
Id = m/24 (l^2+b^2)


M.I. of rectangle about its diagonal is given by m/24 (l^2+b^2).



Hope that is useful...