Moment of Inertia of a Disc

Q.

A circular disc X of radius R is made from an iron plate of thickness t and another disc Y of radius 4R is made from an iron plate of thickness $\frac{t}{4}$ Then the relation between the moment of inertia about their natural axis $I_X$ and $I_Y$ is

1. 

2. 

3. 

4. 

Q. Four identical thin rods each of mass M and length, form a square frame. Moment of inertia offrame about an axis through the centre of the square and perpendicular to its plane is

Q. Moment of inertia of a uniform cylinder of mass M and radius R about its geometric axis is

Q. The moment of inertia of semicircular ring about an axis which is perpendicular to the plane of the ring and passes through the centre

Q. Four rods of equal mass m and length L forms a square ABCD as shown in the figure. The moment of inertia of ABCD about the axis OO passing through the point A lying in the plane of square is

Q. 136.Four identical spheres each of radius 10 cm and mass 1 kg are placed on a horizontal surface touching one another so that their centres are located at the corners of square of side 20 cm. What is the distance of their centre of mass from centre of either sphere?

Q. 87.Linear mass density varies as L=kx .The moment of inertia is maximum for

Q. a hollow sphere is at rest at the top of a rough inclined plane of height h.if it rolls without slipping then rotational kinetic energy of sphere when it reaches at bottomof inclined plane i

Q. 42.A cubical frame is made of 12 rods each of mass m and length l. The moment of inertia of cube about its face diagonal is?

Q. Moment of inertia of a ring of radius R whose mass per unit length varies with parametric angle θ according to the relation λ=λ°cos²θ, about its axis will be

Q. There is a rec†an gular plate of mass M kg of dimensions(a× b)hinged to wall along a.The plate is held in horizontal position by striking n small balls uniformly each of mass m per unit area per unit time. These are striking in shaded half retion of the plate.The balls are colliding elastically with velocity v.What is v?(It is given n=100;M=3kg;m=0.01 kg;b=2m;a=1m;g=10m/s^{

Q. the moment of inertia ofa cube of mass m and side a about one of its edges is equal to

Q. find the moment of inertia of the uniform right angled triangle plate of mass m about the axis AA. height of the triangular plate is h

Q.

The moment of inertia of the uniform semicircular disc of mass $M$ and radius $R$ about a line perpendicular to the plane of the disc through the center is

1. $M{R}^2$

2. $\frac{1}{2}M{R}^2$

3. $\frac{1}{4}M{R}^2$

4. $\frac{2}{5}M{R}^2$

Q. The moment of inertia of a uniform semi circular wire of mass m and radius r about an axis passing through its centre of mass and perpendicular to its plane

Q. 9.Four solid spheres each of mass m and radius r are placed on the vertices of a square of side length a (a>2r) 1) the Moment of inertia of the system about an axis passing through diagnoal of the square will be. 2) The MI of the system about an axis passing through centre of one of the spheres and perpendicular to the plane of square will be.

Q. The ration of rotational to kinetic energy for a hollow sphere in pure rolling motio

Q. From a uniform square lamina of mass M and side L a circular hole of diameter L/2 whose rim passes through the centre of the square is cut the moment of inertia of them remaining part of the square about an axis perpendicular to the plane of lamina and passing through the centre is

Q. a circular hole of radius R/2 is cut off from a solid uniform disc of radius R. If the mass of the remaining portion is M , then the moment of inertia of the body about the axis through O and perpendicular to the plane of a disc is

Q. 81. How to calculate moment of inertia of right angled triangle towards the centre and perpendicular to plane??

Q. a wheel having moment of inertia 2kgm2 about its vertical axis rotates at the rate of 60rpm about its axos the torque which can stop yhe wheel in one minute would b

Q. 42.Can simple harmonic motion take place in a non inertial frame ? If yes , should the ratio of the force applied with the displacement be constant ?

Q. The moment of inertia of a uniform semicircular wire of mass m and radius r, about an axis passing through its center of mass and perpendicular to its plane is

Q. a thin rod of mass M and length L is bent at mid point A to make an angle of 60degree.the moment of inertia of the rod about an axis passing through the point A and perpendicular to the plane of rod would be

Q. A thin disc of mass M and radius R has mass per unit area $\sigma \left(r\right)=k{r}^2$, where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is

1. $\frac{M{R}^2}{2}$
2. $\frac{M{R}^2}{6}$
3. $\frac{M{R}^2}{3}$
4. $\frac{2M{R}^2}{3}$

Q. four thin uniform rods each of length L and mass m are joined to form a square the moment of inertia of square about an axis along its one diagonal

Q. the moment of inertia of a uniform rod of mass M and length l about an axis perpendicular to its length is ml^2/10.the distance of the axis from the centre of the rod is

Q. 23.what is the moment of inertia of a sphere about an axis which is passing through its centre of mass.

Q. ntFour thin uniform rods each of length L and mass m are joined to form a square. The moment of inertia of square about an axis along its one diagonal is?n

Q. three rings each of mass M and radius R are arranged as shown in the figure . the moment of inertia of the arrangement about OO axis