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 $I_x$ and $I_y$ is

1. 
2. 
3. 
4. 

Q. There are two similar discs. One is at rest and the other one is rotating with constant speed about an axis passing through its centre and perpendicular to the plane containing the disc. Which one has larger kinetic energy?

1. Both have same non-zero kinetic energy
2. Both have zero kinetic energy
3. The one at rest.
4. The one which is rotating

Q.

One quarter sector is cut from a uniform disc of radius 'R'. This sector has mass 'M'. It is made to rotate about a line perpendicular to its plane and passing through the center of the original disc. Its moment of inertia about the axis of rotation is

1. 
2. 
3. 
4. 

Q.

Calculate the moment of Inertia of an annular disc of inner radius $R_1$ and outer radius $R_2$ about an axis perpendicular to the plane in which the disc lies and passing through O.

1. 

2. 

3. 

4. 

Q. From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

1. $4M{R}^2$
2. $\frac{40}{4}M{R}^2$
3. $10M{R}^2$
4. $\frac{37}{9}M{R}^2$

Q. A solid sphere of mass M and radius R having a moment of inertia I about its diameter is recast into a solid disc fo radius r and thickness t. The moment of inertia of the disc about an axis passing the edge and perpendicular to the plane remains I. Then R and r are related as

1. $r=\sqrt{\frac{2}{15}}R$
2. $r=\sqrt{\frac{2}{15}}R$
3. $r=\frac{2}{15}R$
4. $r=\frac{2}{\sqrt{15}}R$

Q. Two circular discs A and B are of equal masses and thickness but made of metals with densities $d_A$ and $d_B(d_A>d_B).$ If their moments of inertia about an axis passing through centres and normal to the circular faces be $I_A$ and $I_B$, then

1. 
2. 
3. 
4. 

Q. One quarter sector disc of radius 'R', has mass 'M'. Its moment of inertia about the axis shown in figure is.

1. $\frac{1}{2}M{R}^2$
2. $\frac{1}{4}M{R}^2$
3. $\frac{1}{8}M{R}^2$
4. $\sqrt{2}M{R}^2$

Q. A disc has a mass of 10 kg distribute uniformly and has a radius of 2 m. Moment of inertia about an axis passing through its centre and perpendicular to its plane is.

1. 20 $kg{m}^2$
2. 10 $kg{m}^2$
3. 40 $kg{m}^2$
4. 40 $kg{m}^2$

Q. Five particles of mass 2 kg are attached to the rim of a circular disc of radius 0.1 m and negligible mass. Moment of inertia of the system about the axis passing through the center of the disc and perpendicular to its plane is.

1. $1kg{m}^2$
2. $0.1kg{m}^2$
3. $2kg{m}^2$
4. $0.2kg{m}^2$