Physics · Parallel and perpendicular axes theorems and their applications
Two identical rods each of moment of inertia about a normal axis through centre
Two identical rods each of moment of inertia \( ^{\prime} I^{\prime} \) about a normal axis through centre are arranged in the from of a cross. The \( M . I . \) of the system about an axis through centre and perpendicular to the plane of system is:
- A. \( 2 I \)
- B. \( I \)
- C. 2.5
- D. \( 6 I \)
Step-by-step solution
Each rod has moment of inertia I about an axis through its centre perpendicular to its length. For a rod lying in the plane, the moment of inertia about an axis perpendicular to the plane through its centre is also I. The system axis passes through the common centre, so total moment of inertia = I + I = 2I.