Moment of Inertia of an Annular Disc

Q.

About which of the following axes moment of inertia of a circular disc is minimum?

1. Axis passes through its center and perpendicular to its plane.

2. Axis along the diameter.

3. Axis along the tangent and in its own plane

4. Axis along the tangent and perpendicular to its plane.

Q.

Calculate the moment of Inertia of uniform solid sphere of mass $M$ and Radius $R$, about its diameter

1. 

2. 

3. 

4. 

Q.

The moment of inertia of a uniform cylinder of length $L$ and radius $R$ about its perpendicular bisector is $I$. What is the ratio $\frac{L}{R}$ such that the moment of inertia is minimum?

1. $\sqrt{\frac{3}{2}}$

2. $\frac{\sqrt{3}}{2}$

3. $\frac{2}{3}$

4. $\frac{3}{2}$

Q.

Calculate the moment of Inertia of a solid cylinder of mass '$M$' and radius $R$ about its Axis(as shown)?

1. 

2. 

3. 

4. 

Q. The length of a solid cylinder is $4.5$ times its radius and $I$ is the moment of inertia about its natural axis. This solid cylinder is re-casted into a solid sphere, then the moment of inertia of solid sphere about an axis passing through its centre is :

1. $\frac{5I}{9}$
2. $\frac{10I}{9}$
3. $\frac{9I}{5}$
4. $\frac{9I}{10}$

Q.

Calculate the moment of Inertia of a solid cylinder of mass '$M$' and radius $R$ about its Axis(as shown)?

1. $M{R}^2$

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

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

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

Q. Find the moment of inertial of a solid cylinder of mass $M$ and radius $R$ about a line parallel to the axis of the cylinder and on the surface of the cylinder.

Q. A solid cylinder of mass $20Kg$ has length $1m$ and radius $0.2m$. Then its moment of inertia $(inkg-m^2)$ about its geometrical axis is-

Q. The moment of inertia of a solid sphere of density $\rho$ and radius R about its diameter is

1. $\frac{105}{176}{R}^5\rho$
2. $\frac{105}{176}{R}^2\rho$
3. $\frac{176}{105}{R}^5\rho$
4. $\frac{176}{105}{R}^2\rho$

Q. A bicycle of radius $0.3m$ has a rim of mass $1.0kg$ and $50$ spokes, each of mass $0.01kg$. What is its moment of inertia about its axis of rotation?

Q. A mass $m$ of radius $r$ is rolling horizontally without any slip with a linear speed $v$. It then rolls up to a height given by $\frac{3}{4}\frac{y^2}{g}$

1. the body is identified to be a disc or a solid cylinder
2. the body is a solid sphere
3. moment of inertia of the body about instantaneous axis of rotation is $\frac{3}{2}m{r}^2$
4. moment of inertia of the body about instantaneous axis of rotation is $\frac{7}{5}m{r}^2$

Q. The MI of solid sphere about the tangent is 70 $kg{m}^2$. Its MI about any diameter is -

1. 25 $kg{m}^2$
2. 20 $kg{m}^2$
3. 50 $kg{m}^2$
4. 15 $kg{m}^2$

Q.

Calculate the moment of Inertia of a solid cylinder of mass '$M$' and radius $R$ about its Axis(as shown)?

1. $M{R}^2$

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

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

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

Q. A solid sphere, a thin-walled hollow sphere, a solid cylinder, a thin-walled hollow cylinder and a ring, each of mass $m$ and radius $R$, are simultaneously released at rest from top of an inclined plane, as shown in figure. The objects roll down the plane without slipping. Also we may consider the objects and the surface on which they roll to be perfectly rigid. Match column I and II

Q.

Calculate the moment of Inertia of a solid cylinder of mass '$M$' and radius $R$ about its Axis(as shown)?

1. $M{R}^2$

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

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

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

Q. From a disc of radius $R$ an mass $M$, a circular hole of diameter $R$, whose rim passes through the center is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the center?

1. $\frac{15M{R}^2}{32}$
2. $\frac{13M{R}^2}{32}$
3. $\frac{11M{R}^2}{32}$
4. $\frac{9M{R}^2}{32}$

Q. Moment of inertia of a solid about its geometrical axis is given by $l=\frac{2}{5}M{R}^2$ where $M$ is mass & $R$ is radius. Find out the rate by which its moment of inertia is changing keeping density constant at the moment $R=1m,M=1kg$ & rate of change of radius w.r.t. time $2m{s}^{-1}$

1. $2kg{m}^2{s}^{-1}$
2. $4kgm{s}^{-1}$
3. None of these
4. $4kg{m}^2{s}^{-1}$

Q. The moment of inertia of an uniform solid cylinder about it's geometrical axis is 8 units. The moment of inertia about the axis tangential to one of plane circular faces, i.e., about diameter of the circular base is (length of cylinder is 3 times it's radius)

1. 52 units
2. 26 units
3. 104 units
4. 49 units