Moment of Inertia

From a triangular lamina of side a and mass $m$ , a small triangular Lamina made by joining mid-points of sides of triangular lamina is cut. If Moment of Inertia of complete Lamina about COM is $I_o$ and Moment of Inertia of remaining Lamina about centroid is $\frac{x{I}_0}{16}$, then find the value of $x$.

Four point masses $($each of mass $m$$)$ are arranged in the $X-Y$ plane. The moment of inertia of this array of masses about $Y$-axis is 

The spokes used in a cycle wheel increase its

M.O.I is the ratio of 

A solid sphere, a thin ring and a cylinder of same mass and radius, held at rest are released simultaneously to roll down on an inclined plane. Which one will reach the bottom first?

Point masses $1, 2, 3$ and $4 \mathrm{kg}$ are lying at the points $(0, 0, 0), (2, 0, 0), (0, 3, 0)$ and $(-2, -2, 0)$, respectively. The moment of inertia of this system about the $x$-axis will be,

Four similar point masses (each of mass $m$) are placed on the circumference of a disk of mass $M$ and radius $R$. The moment of inertia of the system about the normal axis through the center $O$ will be,

On the marks of $20 \mathrm{cm}$ and $70 \mathrm{cm}$ of a light meter scale, two weights, $1 \mathrm{kg}$ and $4 \mathrm{kg}$, respectively, are placed. The moment of inertia (in $\mathrm{kg} {\mathrm{m}}^2$) about the vertical axis through the $100 \mathrm{cm}$ mark will be,

M.O.I is the ratio of 

M.O.I. of a disc is minimum about an axis 

A solid cylinder of uniform density of radius $2 \mathrm{cm}$ has a mass of $50 \mathrm{g}$. If Its length is $12 \mathrm{cm}$, Calculate Its Moment of Inertia about an axis passing through its centre and perpendicular to its length.

The moment of inertia of a solid cylinder of mass $M$, radius $R$ and length $L$ about a transverse axis passing through its centre is:

What are the dimensions of radius of gyration.

The SI unit of radius of gyration is

For a ring of mass $50 \mathrm{g}$ and radius $20 \mathrm{cm}$. What will be the moment of inertia of the ring about a tangent in the plane of the circle of the ring?

There is a ring of mass $M$ and radius $R$. What will be its moment of inertia about a tangent parallel to the diameter?

A circular disc is to be made by using iron and aluminium, so that it acquires maximum moment of inertia about its geometrical axis. It is possible with

The Moment of inertia of a uniform angular with mass $m$, thickness $t$ and inner and outer radius as $R_1$ and $R_2$ respectively can be expressed as

The moment of inertia of a ring about one of its diameter is $5 \mathrm{kg} {\mathrm{m}}^2$ ? What will be its moment of inertia about a tangent parallel to the diameter?

The moment of inertia of a ring about one of its diameter is $I$. What will be its moment of inertia about a tangent parallel to the diameter?