MHT CET202519 Apr 2025Morning ShiftPhysicsRotational MotionActual
Four particles each of mass M are placed at the corners of a square of side L . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is
Options
- AL
- BL 2
- CL 4
- DL 2
Correct answer
D. L 2
Step-by-step solution
The system consists of four particles of mass M arranged at the corners of a square of side L . The rotation axis is perpendicular to the square's plane and passes through its center. The distance r from each corner to the center is half the diagonal length. The diagonal is L 2 , so r = L/ 2 . The moment of inertia for one particle about this axis is Mr^2 = M(L^2 / 2) = ML^2 / 2 . For four identical particles, the total moment of inertia is I_ total = 4(ML^2 / 2) = 2ML^2 . The total mass is M_ total = 4M . The radi