Three identical rods each of mass ‘M’ and length ‘L’ are joined to form a symbol ‘H’. The moment of inertia of the system about one of the sides of ‘H’ is

Step-by-step solution

The given situation can be shown as Let us take the moment of inertia of the system about rod R 1 then total moment of inertia is For rod R 1 l 1 = 0 For rod R 2 , using perpendicular axis theorem, l 2 = M L 2 3 For rod R 3 , using parallel axis theorem, l 3 = l C M + l a t L = 0 + M L 2 = M L 2 Now, putting the values of l 1 , l 2 and l 3 in Eq. (i), we get l τ = 0 + M L 2 3 + M L 2 ⇒ l τ = 4 M L 2 3