question_answer

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

A) \[\frac{\pi }{12}M{{R}^{2}}\]

B)              \[\left( \frac{4}{3}-\frac{\pi }{4} \right)M{{R}^{2}}\]

C) \[\left( \frac{4}{3}-\frac{\pi }{6} \right)\,M{{R}^{2}}\]               

D) \[\left( \frac{8}{3}-\frac{10\pi }{16} \right)\,M{{R}^{2}}\]