Moment of Inertia of a Ring

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.

A solid sphere of mass $m$, radius$r$, and having a moment of inertia about an axis passing through the center of mass as$I$ is recast into a disc of thickness $t$, whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains $I$. Then, the radius of the disc will be

Q.

Find the moment of Inertia of a uniform hollow sphere of mass $M$ and radius $R$, about its diameter

1. 

2. MR²

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. A thin uniform rod of mass $M$ and length $L$ has its moment of inertia $I_{rod}$ about its perpendicular bisector. This rod is bend in the form of a circular shape of radius $r$. Now, circle has its moment of inertia $I_{\text{circle}}$ about its centre and perpendicular to its plane. Find the ratio of $I_{rod}:I_{\text{circle}}$.

1. $\frac{{\pi }^2}{3}$
2. $\frac{{\pi }^2}{12}$
3. $\frac{{\pi }^2}{4}$
4. $1$

Q.

Which of the following has the highest moment of inertia?

1. A disc about any of its diameters

2. A ring about any of its diameters

3. A solid sphere about any of its diameters

4. A hollow sphere about any of its diameters

Q. A system of a circular disc of mass $900\text{g}$ and radius $4\text{m}$ and a circular ring of mass $2\text{kg}$ and radius $5\text{m}$ are stacked about their common centre as shown in figure. What is the moment of inertia of the system about an axis passing through their common centre perpendicular to the plane of the disc and the ring?

1. $65.4{\text{kgm}}^2$
2. $54.2{\text{kgm}}^2$
3. $50{\text{kgm}}^2$
4. $57.2{\text{kgm}}^2$

Q. A disc has a mass of 10 kg distribute uniformly and has a radius of 2m. What will be its moment of inertia about an axis passing through its centre and perpendicular to its plane?

1. 20 $kg-m^2$
2. 10 $kg-m^2$
3. 40 $kg-m^2$
4. None of these

Q. Two bodies with moment of inertias $I_1$ and $I_2$ $(I_1>I_2)$ have equal angular momenta. If K.E. of rotation are $E_1$ and $E_2$ then

1. $E_1=E_2$
2. $E_1>E_2$
3. $E_1<E_2$
4. $E_1\ge E_2$

Q. $I_A,I_B$ and $I_C$ are the moments of inertia of a ring, semicircular ring and an arc of the same mass about the axes as shown below. Which of the following options is correct?

1. $I_A>I_B>I_C$
2. $I_A<I_B<I_C$
3. $I_A=I_B=I_C$
4. $I_A>I_B=I_C$

Q. Four identical rods of mass $M=6\text{kg}$ each are welded at their ends to form a square and then welded to a massive ring having mass $M=4\text{kg}$ and radius $R=1\text{m}$. If the system is allowed to roll down the incline of inclination $\theta ={30}^{\circ }$.


The acceleration of the system will be

1. $\frac{g}{2}$
2. $\frac{g}{4}$
3. $\frac{7g}{24}$
4. $\frac{g}{8}$

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. $\frac{M}{6}\{R_2^2+R_1^2\}$

2. $\frac{M}{2}\{R_1^2+R_2^2\}$
3. $\frac{M}{4}\{R_1^2+R_2^2\}$
4. $\frac{M}{2}{\{R_1+R_2\}}^2$

Q. A thin uniform rod of mass $M$ and length $L$ has its moment of inertia $I_{rod}$ about its perpendicular bisector. This rod is bend in the form of a circular shape of radius $r$. Now, circle has its moment of inertia $I_{\text{circle}}$ about its centre and perpendicular to its plane. Find the ratio of $I_{rod}:I_{\text{circle}}$.

1. $\frac{{\pi }^2}{3}$
2. $\frac{{\pi }^2}{12}$
3. $\frac{{\pi }^2}{4}$
4. $1$