Moment of Inertia of Hollow Sphere

Q. 6.The figure shows an isoceles triangular plate of mass M and base L. The angle at the apex is 90. The apex lies at the origin and the base is parallel to x-axis. Find the moment of inertia of the plate about : * z axis * x axis * y axis * about its base parallel to x-axis

Q. Moment of inertia of a disc about an axis which is tangentand parallel to its plane is I. Then, the moment of inertia ofdisc about a tangent, but perpendicular to its plane will be

Q. 2) Two circular disc of same mass and thickness are made from metals having densities p, and p, respectively. The ratio of their moment of inertia about an axis passing through its centre is

Q. 22. A disc of radius R and thickness R/6 has moment of inertia I about an Axis passing through its centre and perpendicular to its plane. Disc is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is :- A. I/5 B. I/6 C. I/32 D. I/64

Q. 24. Four spheres of diameter 2a and mass M areplaced with their centres on the four corners ofasquare of side b. Then moment of inertia of thesystem about an axis about one of the sides of thesquare is(1) Ma2+ 2Mb2(2) Ma2(3) Ma2 + 4Mb2(4)Ma2+ 2Mb2

Q.

Two identical spheres each of mass 1.20 kg and radius 10.0 cm are fixed at the ends of a light rod so that the separation between the centres is 50.0 cm. Find the moment of intertia of the system about an axis perpendicular to the rod passing through its middle point.

1. 0.19kg - m²

2. 160kg - m²

3. 190kg - m²

4. 0.16kg - m²

Q. A sphere of mass 10kg and radius 0.5 m rotates about a tangent The moment of inertia of the solid sphere is

Q. A uniform metallic rod rotates about its perpendicular bisector with constant angular speed. If it is heated uniformly to raise its temperature slightly:- (1) Its speed of rotation increases(2) Its speed of rotation decreases(3) Its speed of rotation remains same(4) Its speed of rotation increases because itsmoment of inertia increases

Q. 5.From a circular disc of radius R and mass 4Ma small disc of radius is removed from the discas shown. The moment of inertia of the remainingdisc about an axis perpendicular to the plane of thedisc and passing through O is2(1) MR13(2) MR2(3) MR4(4) MR

Q. The moment of inertia of a flat annular ring havingmass M, inner radius a and outer radius b aboutthe diametric axis through the centre is

Q. 44. find the moment of inertia of @ pair of spheres, each having a mass m and radius r kept in contact about tangent passing through the point of contact

Q.

A solid cylinder of 200g and radius 10 cm has a moment of inertia (about its natural axis)

1. 10^-3 kg m²

2. 3.0 x 10^-3 kg m²

3. 2.0 x 10^-3 kg m²

4. 2.5 x 10^-3 kg m²

Q. 3. From a disc of radius R and mass M, a circular hole of radius R/4 is removed from a distance 3R/4 from centre. What will be the moment of inertia of remaining part of disc about an axis perpendicular to plane and passing through centre of original disc ?

Q. 7) A ring and a thin hollow cylinder have the same mas sand radius. If I_r and I_s, represent their moment of inertia about their axes, then relation between them is?

Q. Derive moment of inertia of a cube

Q. The moment of inertia of a solid sphere has its radius of gyration R about a certain axis. Find the distance of that axis from centre of solid sphere

Q. The moment of inertia of solid sphere of mass M and radius R about any †an gent is l0 . The moment of inertia about any diameter sphere i

Q. moment of inertia of a thin uniform rod of length l and mass m about an axis passing through a point at a distance of l/4 from centre O and at an angle of 60 to the rod is

Q. If the moment of inertia of a solid sphere about any †an gent is I, then the moment of inertia about its any diameter is Options: a-5I/7 B-2I/5 C-2I/7 D-5I/7

Q. 87. From a uniform disc of radius R and mass 9m, a small disc of radius R/3 is removed.What is the moment of inertia of remaining disc about an axis passing through the centre of discri and perpendicular to its plane?

Q. Three rods are joined to form an equilateral triangle having side L. If each rod has m .find moment of inertia about an axis passing through centre of mass and perpendicular to plane of structure(by both perpendicular axis theorem and by parallel axis theorem).?

Q.

What is the moment of inertia of a solid sphere about its diameter?

1. 

2. 

3. 

4. 

Q. Moment of inertia of a solid cube about its body diagonal.

Q.

The moment of inertia of two spheres of equal masses is equal. If one of the spheres is solid of radius √45 m and the other is a hollow sphere. What is the radius of the hollow sphere?

1. √3 m

2. 3 m

3. 3√3 m

4. 5 m

Q. find moment of inertia about an edge of a cube

Q. 64. From a disc of radius r and mass m a circular hole of diameter r whose rim pass through the centre is cut .The moment of inertia of remaining part of the disc about a perpendicular axis passing through centre is

Q. Two identical solid spheres each of mass $1.20\text{kg}$ and radius $10.0\text{cm}$ are fixed at the ends of a light rod so that the separation between the centres is $50.0\text{cm}$. Find the moment of inertia $\left({\text{kgm}}^2\right)$ of the system about an axis perpendicular to the rod passing through its middle point.

Q. 34. The minimum moment of inertia of solid sphere about any axis is 2/5 mr square.then its radius of gyration about an axis at distance 2r from centre will be?

Q. Two spheres each of mass $M$ and radius $\frac{R}{2}$ are connected with a massless rod of length $R$ as shown in the figure. The moment of inertia of the system about an axis $\left(Y{Y}^{\prime }\right)$ passing through the centre of one of the spheres and perpendicular to the rod is

1. $\frac{21}{5}M{R}^2$
2. $\frac{2}{5}M{R}^2$
3. $\frac{5}{2}M{R}^2$
4. $\frac{5}{21}M{R}^2$

Q. moment of inertia of a hallow sphere of mass M and inner radius R and outer radius 2R having uniform mass distribution about diameter axis is