$A$ ring of mass $m$ and radius $r$ is melted and recast into a sphere. The moment of inertia of the sphere will be:

The figure shows an isosceles triangular plate of mass $M$ and base $L$. The angle at the apex is $90^o$. The apex lies at the origin and the base is parallel to the $X$-axis. The moment of inertia of the plate about the $y$-axis is:

$A$ thin uniform wire of mass $m$ and linear mass density $\rho$ is bent in the form of a circular loop. The moment of inertia of the loop about its diameter is

Four particles of masses $5 \ kg, 2 \ kg, 3 \ kg$,and $4 \ kg$ are placed at $(0, 0, 0), (2, 0, 0), (0, 3, 0)$,and $(-2, -2, 0)$ respectively. The moments of inertia about the $x$-axis,$y$-axis,and $z$-axis respectively are:

$A$ solid sphere of mass $M$ and radius $R$ is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius $2R$. The second part is converted into a uniform solid sphere. Let $I_1$ be the moment of inertia of the disc about its axis and $I_2$ be the moment of inertia of the new sphere about its axis. The ratio of $I_1/I_2$ is given by

If the radius of a solid sphere is $35\,cm,$ calculate the radius of gyration when the axis is along a tangent.