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 

What is the necessity of radius of gyration?

What are the physical significance of radius of gyration?

What is the physical significance of moment of inertia? Is radius of gyration a constant quantity?

In the calculation of the radius of gyration, we use intensity of loadings. So whenever the distributed loading acts perpendicular to an area its intensity varies

The physical significance of the moment of inertia is similar to the _________________ in the translational motion ?

Inertia is the resistance of any physical object to any change in its_____. 

Moment of inertia, in physics, quantitative measure of the rotational inertia of a body.This statement is true or false?

What is moment of inertia give its significance ?

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,

Write the three equations of motion for a particle that undergoes rotational motion.

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

A uniform thin rod $\mathrm{AB}$ of length $L$ and mass $m$ is undergoing rotation about a fixed axis passing through end $\mathrm{A}$ and perpendicular to the rod, such that end $\mathrm{A}$ remains stationary as shown. The kinetic energy of section $\mathrm{AP}$ of the rod is equal to the kinetic energy of section $\mathrm{BP}$ of the rod at an instant. Then what is the value of ${\left(\frac{\mathrm{A}\mathrm{B}}{\mathrm{AP}}\right)}^3$?

($\mathrm{AB}$ and $\mathrm{AP}$ are lengths of respective parts of the rod)

Two identical water bottles one empty and the other filled with water are allowed to roll down an inclined plane. Which one of them reaches the bottom first? Explain your answer.

The radius of gyration of a body about an axis, at a distance of $0.4 \mathrm{m}$ from its centre of mass is $0.5 \mathrm{m}$. Radius of gyration about a parallel axis passing through its centre of mass is 

A table has a heavy circular top of radius $1 \mathrm{m}$ and mass $20 \mathrm{kg}$ placed on four light (considered massless) legs placed symmetrically on its circumference. The maximum mass that can be kept anywhere on the table without toppling it is close to

Which one is the correct expression for radius of gyration where $I$ is the moment of inertia and $m$ is the mass of the body?

Four particles, each of mass $\text{'}m\text{'}$ are situated at the vertices of a square $ABCD$ of side $\text{'}a\text{'}$ as shown in the figure. The moment of inertia of the system about line $BD$ will be