Three rods each of length $L$ and mass $M$ are placed along $X$,$Y$,and $Z$-axes in such a way that one end of each rod is at the origin. The moment of inertia of this system about the $Z$-axis is

Five masses,each of $2\, kg$,are placed on a horizontal circular disc,which can be rotated about a vertical axis passing through its centre. All the masses are equidistant from the axis at a distance of $10\, cm$. The moment of inertia of the whole system (in $g\cdot cm^2$) is: (Assume the disc is of negligible mass)

Two point masses of $0.3 \ kg$ and $0.7 \ kg$ are fixed at the ends of a rod of length $1.4 \ m$ and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum is located at a distance of

Match List-$I$ with List-$II$:

List-$I$	List-$II$
$(A)$ Moment of inertia of solid sphere of radius $R$ about any tangent	$(I)$ $\frac{5}{3} MR^2$
$(B)$ Moment of inertia of hollow sphere of radius $R$ about any tangent	$(II)$ $\frac{7}{5} MR^2$
$(C)$ Moment of inertia of circular ring of radius $R$ about its diameter	$(III)$ $\frac{1}{4} MR^2$
$(D)$ Moment of inertia of circular disc of radius $R$ about any diameter	$(IV)$ $\frac{1}{2} MR^2$

Choose the correct answer from the options given below:

For the same total mass,which of the following will have the largest moment of inertia about an axis passing through its centre of mass and perpendicular to the plane of the body?

$A$ circular disc of radius $R$ and thickness $R/8$ has a moment of inertia $I$ about an axis passing through its centre and perpendicular to its plane. It is melted and recast into a solid sphere. The moment of inertia of the sphere about an axis passing through its diameter is: