Four spheres each of diameter $2a$ and mass $M$ are placed with their centres on the four corners of a square of side $b$. Then the moment of inertia of the system about an axis along one of the sides of the square is

Three balls of masses $2 \,kg$,$4 \,kg$,and $6 \,kg$ are placed at the midpoints of the sides of an equilateral triangle of side length $2 \,m$. The moment of inertia of the system about an axis passing through the centroid and perpendicular to the plane of the triangle is . . . . . .$kg \,m^2$.

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

Three identical thin rods each of mass $m$ and length $l$ are placed along $x, y$ and $z$-axes respectively. They are placed such that one end of each rod is at the origin $O$. The moment of inertia of this system about the $z$-axis is:

From a uniform wire,two circular loops are made: $(i)\ P$ of radius $r$ and $(ii)\ Q$ of radius $nr$. If the moment of inertia of $Q$ about an axis passing through its center and perpendicular to its plane is $8$ times that of $P$ about a similar axis,the value of $n$ is (diameter of the wire is very much smaller than $r$ or $nr$).

$A$ flywheel is constructed such that its entire mass is concentrated at the rim because: