Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $K_{c}$. Radius of gyration of the same disc about a diameter of the disc is $K_d$. The ratio $K_c: K_d$ is

$A$ straight rod of length $L$ is made of a material having mass per unit length $m(x) = \lambda|x|$, where $x$ is measured from the center of the rod. The moment of inertia about an axis perpendicular to the rod and passing through one end of the rod is to be calculated. Given $L = 1 \ m$ and $\lambda = 16 \ kg/m^2$.

Three thin uniform rods,each of mass $M$ and length $L$,are placed along the three Cartesian axes such that one end of each rod is at the origin. Find the moment of inertia of this system about the $z$-axis.

Four small objects, each of mass $m$, are fixed at the corners of a rectangular wire-frame of negligible mass with sides $a$ and $b$ $(a > b)$. If the wire frame is now rotated about an axis passing along the side of length $b$, then the moment of inertia of the system for this axis of rotation is:

Three point masses $m_1, m_2$,and $m_3$ are placed at the vertices of an equilateral triangle of side $a$. Find the moment of inertia of this system about the altitude passing through $m_1$.

If $I_1, I_2$ and $I_3$ are moments of inertia of a solid sphere,a hollow sphere,and a ring of the same mass $M$ and radius $R$ about their respective geometrical axes,which of the following statements holds true?