Two circular loops $A$ and $B$ of radii $R$ and $NR$ respectively are made from a uniform wire. The moment of inertia of $B$ about its axis is $3$ times that of $A$ about its axis. The value of $N$ 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)

What is the radius of gyration of a circular disc of radius $R$ about an axis passing through its center and perpendicular to its plane?

Three point masses $m_1, m_2, m_3$ are located at the vertices of an equilateral triangle of side length $a$. The moment of inertia of the system about an axis along the altitude of the triangle passing through $m_1$ is:

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:

An iron circular disc $X$ has radius $R$ and thickness $t$. Another iron circular disc $Y$ has radius $4R$ and thickness $t/4$. The relationship between the moments of inertia $I_X$ and $I_Y$ of these two discs is .......