Three thin rods, each mass ' 2 M ' and length ' L ' are placed along x, y and z axis which are mutually perpendicular. One end of each rod is at origin. Moment of inertia of the system about x -axis is

Step-by-step solution

Total moment of inertia, I _ total = I _ x + I _ y + I _ z ...(i) Moment of inertia of thin rod, when axis is passing through one end and perpendicular to the rod, I = ML ^2 3 ...(ii) I _ y = M _ y L ^2 3 = 2 ML ^2 3 ...[From(ii)] ... (given, M _ y =2 M ) Similarly, I _ z = M _ 2 L ^2 3 = 2 ML ^2 3 ...[From(ii)] ( . given, . M _ z =2 M ) I _ x =0 ( Rod lies along X -axis ) Substituting in (i), I _ total = 4 ML ^2 3