Question

AB and CD are two identical rods each of length (L) and mass (m) joined to form a cross is fixed inside a ring of mass (m) and radius (L/2). Moment of inertia of the system about a bisector of the angle between the rods is -

Answer 1

Answer:

The moment of inertia of rods AB and CD along an axis perpendicular to the rods' plane and passing through their point of intersection O is XY, and X'Y' are two mutually perpendicular axes in the plane of the two rods crossing through O.

Explanation:

• The moment of inertia of the coupled rods is I0=mI212+mI212=mI26 around an axis passing through their point of intersection O and perpendicular to the rods' plane.
• Now, xy and are two mutually perpendicular axes passing through O in the plane of two rods. Then there's the issue of symmetry.