The moment of inertia of a thin uniform rod of mass ' M ' and length ' L ', about an axis perpendicular to length of the rod and at a distance ' L / 4 ' from one end is

Step-by-step solution

Moment of inertia via parallel axis theorem: The moment of inertia about the center of mass axis is I_ CM = ML^2 12 . The distance from the given axis to the center of mass is d = | L 2 - L 4 | = L 4 . Applying the parallel axis theorem I = I_ CM + Md^2 : I = ML^2 12 + M ( L 4 )^2 = ML^2 12 + ML^2 16 Combining terms with common denominator 48: I = 4ML^2 48 + 3ML^2 48 = 7ML^2 48 Final moment of inertia: 7ML^2 48