Question

21. three identical uniform rods each of length l are joined to form a rigid equilateral triangle .its radius of gyration about an axis passing through a corner and perpendicular to the plane of the triangle is

Answer 1

Mol of rod passing through the center= 1/12 ML²
Mol of rod passing through one side= 1/3 ML²

AP= √3/2 L

Mol of BC through the prependicular A
= 1/12 ML² + M(√3/2 L)²
= 1/12 ML² + √3/4 ML²
= 5/6 ML²

By the principle of superposition
= 1/3 ML² + 1/3 ML² + 5/6 ML²
= 9/6ML²
= 3/2 ML²

radius of gyration
k = √3/2 ML²/ 3M
= L/√2

Answer 2

Your answer is L/square root 3