Question

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 $OO ^{\prime}$ is $\frac{ x }{4} Ma ^2$. Then, the value of $x$ will be ___

Answer 1

$ I_1=I_3=\frac{M^2}{4} $
$ I_2=\frac{M R^2}{4}+M R^2=\frac{5}{4} M R^2=I_4$

So $I = I _1+ I _2+ I _3+ I _4$
$ =\frac{ MR ^2}{2}+\frac{5}{2} MR ^2 $
$ =3 MR ^2, \text { Putting R }=\frac{ a }{2} $
$ I =\frac{3 Ma ^2}{4}, \text { So } x =3$