Four identical discs each of mass ' M ' and diameter ' a ' are arranged in a small plane as shown in figure. If the moment of inertia of the system about O O ' is x 4 M a 2 . Then, the value of x will be _____ .

Step-by-step solution

Considering four identical discs as 1 ,   2 ,   3 and 4 . Moment of inertia of disc about diagonal is I 1 = I 3 = M R 2 4 Now using parallel axis theorem, Moment of inertia of disc 2 and 4 is I 2 = I 4 = M R 2 4 + M R 2 = 5 4 M R 2 So, net moment of inertia about O O ' is I = I 1 + I 2 + I 3 + I 4 = 2 M R 2 4 + 2 5 4 M R 2 = M R 2 2 + 5 2 M R 2 = 3 M R 2 Putting R = a 2 I = 3 M a 2 4 , so, x = 3