MHT CET202527 Apr 2025Evening ShiftPhysicsRotational MotionActual
A thin wire of length ' L ' and uniform linear mass density ' ' is bent into a circular ring. The moment of inertia of ring about a tangential axis in its plane is
Options
- A3 L^2 8 ^2
- B8 ^2 3 L^3
- C3 L^3 8 ^2
- D8 ^2 3 L^2
Correct answer
A. 3 L^2 8 ^2
Step-by-step solution
Given a wire of length L with uniform linear mass density , the total mass is M = L . When formed into a circular ring, the circumference equals the wire length, so L = 2 R and R = L 2 . The moment of inertia about a diameter is I_d = MR^2 2 by the perpendicular axis theorem. Applying the parallel axis theorem for a tangential axis in the plane, located distance R from the center: I_ tangential = I_d + MR^2 = MR^2 2 + MR^2 = 3 2 MR^2 . Substituting M = L and R = L 2 : I_ tangential = 3 2 ( L) ( L 2 )^2 = 3 L^3 8 ^2