Four holes of radius R are cut from a thin square plate of side 4 R and mass M . The moment of inertia of the remaining portion about z -axis is

Step-by-step solution

If M is mass of the square plate before cutting the holes, then mass of portion of each hole, m= M 16 R^2 R^2= M 16 Moment of inertia of remaining portion about Z axis aligned & I=I_ square -4 I_ hole & = M 12 (16 R^2+16 R^2 )-4 [ m R^2 2 +m( 2 R)^2 ] & = M 12 32 R^2-10 m R^2 & = 8 3 M R^2- 10 16 M R^2 & I= ( 8 3 - 10 16 ) M R^2 . aligned