Calculation of 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 $x$.

What is moment of inertia of ring about tangent?

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?

There is a solid cylinder of uniform density having radius $2 \mathrm{cm}$ has a mass of $50 \mathrm{g}$. If Its length is $12 \mathrm{cm}$,

Calculate Its Moment of Inertia (In terms of$\times {10}^{-5} \mathrm{kg} {\mathrm{m}}^2$) about an axis passing through its centre and perpendicular to its length. 

A solid cylinder of uniform density of radius $4 \mathrm{cm}$ has a mass of $100 \mathrm{g}$. If Its length is $24 \mathrm{cm}$, Calculate its moment of inertia $(\mathrm{g}.{\mathrm{cm}}^2)$ about an axis passing through its centre and perpendicular to its length.

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.

Calculate the moment of inertia of a solid cylinder of mass $M$, radius $R$ and length $L$ about a transverse axis passing through its centre.

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:

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?

Calculate the Moment of Inertia of an annular disc of mass $M$ and inner radius $R_1$ and outer radius $R_2$about an axis tangential and perpendicular to the plane.

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 uniform circular ring of mass $M$ and radius $R$ about its diameter is _____ $M{R}^2$.

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?

A solid cylinder is made of radius R and height 3R having mass density $\rho$ . Now two half spheres of radius R are removed from both ends. The moment of inertia of remaining portion about axis ZZ' can be calculated as $\frac{29}{6K}\pi R^5\rho$ . Find K.

A uniform thin bar of mass $6 \mathrm{kg}$ and length $2.4$ meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ________ $\times {10}^{-1} \mathrm{kg} {\mathrm{m}}^2$

The moment of inertia of a rigid body depends on:

Let $I_1$ and $I_2$ be the moments of inertia of two bodies of identical geometrical shape, the first made of aluminium and the second of iron. Then, which of the following statements is true?

A closed cylindrical tube containing some water (not filling the entire tube) lies in a horizontal plane. If the tube is rotated about a perpendicular bisector, what happens to the moment of inertia of water about the axis?