Moment of Inertia

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 

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 

What are the dimensions of radius of gyration.

The SI unit of radius of gyration is

The SI unit of moment of inertia of a solid sphere is $\mathrm{kg} {\mathrm{m}}^3$

Four hollow spheres, each with a mass of $1 \mathrm{kg}$ and a radius $\mathrm{R}=10\mathrm{cm},$ are connected with massless rods to form a square with side of length $\mathrm{L}=50 \mathrm{cm},$ In case-1, the masses rotate about an axis that bisects two sides of the square. In case- 2, the masses rotate about an axis that passes through the diagonal of the square, as shown in the figure. Compute the ratio of the moments of inertia ${\mathrm{I}}_1/{\mathrm{I}}_2,$ for the two cases.

The distance in the parallel axis theorem is multiplied by _____.

The moment of inertia of a hollow cubical box of mass $M$ and side length $a$, about an axis passing through centres of two opposite faces, is equal to $\frac{xM{a}^2}{18}$. The value of $x$ is

These questions consists of two statements each printed as Assertion and Reason. While answering these questions you are required to choose any one of the following five responses.

Assertion: If we draw a circle around the centre of mass of a rigid body, then moment of inertia about all parallel axes passing through this circle has a constant value.
Reason: Dimensions of radius of gyration are $\left[{\mathrm{M}}^0{\mathrm{LT}}^0\right]$

A closed cylindrical container is partially filled with water. As the container rotates in a horizontal plane about a perpendicular, its moment of inertia

The inductance in a coil plays the same role as

The moment of inertia of a hollow cubical box of mass $M$ and side length $a$, about an axis passing through centres of two opposite faces, is equal to $\frac{xM{a}^2}{18}$. The value of $x$ is

The moment of inertia of a thin rod of length $L$ and mass $M$ about an axis passing through a point at a distance $\frac{L}{3}$ from one of its ends and perpendicular to the rod is,

Three solid spheres of mass $M$ and radius $R$ are shown in the figure. The moment of inertia of the system about $xx\text{'}$ axis will be,