Four point masses, each of mass (M ) are placed at the corners of a square of side (L ). The moment of inertia of the system about one of its diagonals is

Step-by-step solution

The given masses are shown in the figure. Mass of each point mass (=M ) (A B=B C=C D=D A=L ) Length of diagonal ( aligned B D & = D A^2+A B^2 & = L^2+L^2 & = 2 L^2 =L 2 O D & =O B= B D 2 = L 2 2 = L 2 aligned ) ( ) Moment of inertia of given system about the diagonal (A C ) ( aligned I_ A C & =I_A+I_B+I_C+I_D & =0+M ( L 2 )^2+0+M ( L 2 )^2 & = M L^2 2 + M L^2 2 =M L^2 aligned )