MHT CET202312 May 2023Evening ShiftPhysicsRotational MotionActual
A thin wire of length ' L ' and uniform linear mass density ' m ' is bent into a circular coil. The moment of inertia of this coil about tangential axis and in plane of the coil is
Options
- A3 ~mL ^2 5 ^2
- B3 mL^3 8 ^2
- C3 ~mL ^3 4 ^2
- D3 ~mL ^2 7 ^2
Correct answer
B. 3 mL^3 8 ^2
Step-by-step solution
Moment of inertia of thin wire: aligned I & = MR ^2 2 M & = V m and L =2 R R & = L 2 I & = Lm 2 ( L 2 )^2 I & = mL ^3 8 ^2 aligned Using Parallel axis theorem: aligned & I^ =I+M R^2 & I= mL^3 8 ^2 +L m ( L 2 )^2 & I= 3 mL^3 8 ^2 aligned