Question

Three point masses M₁, M₂ and M₃ are located at the vertices of an equilateral triangle of side 'a'. What is the moment of inertia of the system about an axis along the attitude of the triangle passing through M₁ ? 

(A) (M₁ + M₂) (a² / 4) 

(B) (M₂ + M₃) (a² / 4) 

(C) (M₁ + M₃) (a² / 4) 

(D) (M₁ + M₂ + M₃) (a² / 4)

Answer 1

Correct option: (B) (M₂ + M₃) (a² / 4) 

Explanation:

To find: The moment of inertia about AD.

I = M₁ (Perpendicular distance of M₁ from AD)² + M₂ (Perpendicular distance of M₂ from AD)² + M₃ (Perpendicular distance of M₃ from AD)² 

= M₁(0) + M₂(a/2)² + M₃(a/2)² 

= (M₂ + M₃) (a² / 4)