Parallel Axis Theorem

Q. Moment of inertia of a uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

1. 5 l
2. 6 l
3. 3 l
4. 4 I

Q. moment of inertia of an uniform rod of length L and mass m about an axis through one end at an angle 45degree to rod is

Q. Two uniform rods of mass m and length T form across, moment of inertia of cross about an axisparallel to CD passing through A is

Q. The moment of inertia about hinge axis of a wheel of radius 20 cm is 40 kgm2.if atangential force of 100N is applied on rim of the wheel.then its angular acceleration will be

Q. A T joint is formed by two identical rods A and B each of mass M and length L in the X Y plane .its moment of inertia about axis coinciding with A is.

Q. It is easier to pull a lawn mover than to push it.Explain why

Q. 34. Moment of inertia about axis 3 , which is also parallel to the diameter if this is a solid hemisphere

Q. moment of inertia is a 1. tensor quantity 2, scalar 3. vector 4.none and if tensor is not mentioned then it is which quantity

Q. There are four solid balls with their centres at the four corners of a square of side $a$. The mass of each sphere is $m$ and radius $r$. Find the moment of inertia of the system about one of the sides of the square.

1. $\frac{8}{5}m{r}^2+2m{a}^2$
2. $\frac{5}{8}m{r}^2+2m{a}^2$
3. $m{r}^2+\frac{8}{5}m{a}^2$
4. $m{r}^2+\frac{5}{8}m{a}^2$

Q. Find the MOI of a uniform circular disc of mass $M=10\text{kg}$ and radius $R=10\text{m}$ about tangent perpendicular to its plane.

1. $1200{\text{kg m}}^2$
2. $1500{\text{kg m}}^2$
3. $1400{\text{kg m}}^2$
4. $1000{\text{kg m}}^2$

Q. dimensional formula of mobility

Q.

The moment of inertia is given about an axis perpendicular to the plane of a circular disc. To find the moment of inertia about an axis along a diameter use the _____________.

Q. A lamina is made by removing a small disc of diameter $2R$ from a bigger disc of uniform mass density of radius $2R$ as shown in the figure. The moments of inertia of this lamina about an axis passing through $\text{O}$ and $\text{P}$ are $I_0$ and $I_P$ respectively. Both these axes are perpendicular to the plane of the lamina. The ratio $\frac{I_P}{I_O}$ is

1. $\frac{37}{8}$
2. $\frac{37}{13}$
3. $\frac{8}{13}$
4. $\frac{1}{4}$

Q. The moment of inertia of a square lamina of side A and mass M about an axis passing through center of mass and perpendicular to the plane is

Q. how to find the moment of inertia of about an axis which passes at an angle to a disc

Q. Four holes of radius $R$ each are cut from a thin square plate of side $4R$ and mass $M$. The moment of inertia of the remaining portion about $z-$ axis (out of the plane) is

1. $\frac{\pi }{12}M{R}^2$
2. $(\frac{4}{3}-\frac{\pi }{4})M{R}^2$
3. $(\frac{8}{3}-\frac{10\pi }{16})M{R}^2$
4. $(\frac{4}{3}-\frac{\pi }{6})M{R}^2$

Q. The moment of inertia of a hollow cylinder of radius $R$ and mass $M$ about an axis passing through the outer circumference along the height of the hollow cylinder is

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

Q.
Two masses of 8 kg & 4 kg are connected by a light rod of length 30 cm. Moment of inertia of system about an axis perpendicular to rod is I. Minimum value of I is

1. $24\times {10}^{-2}kg{m}^2$
2. $36\times {10}^{2}kg{m}^2$
3. $48\times {10}^{-2}kg{m}^2$
4. $108\times {10}^{-2}kg{m}^2$

Q. Three rods each of mass $m$ and length $L$ are joined to form an equilateral triangle as shown in the figure. What is the moment of inertia about an axis passing through the centre of mass of the system and perpendicular to the plane?

1. $2m{L}^2$
2. $\frac{m{L}^2}{2}$
3. $\frac{m{L}^2}{3}$
4. $\frac{m{L}^2}{6}$

Q. what are inertial and non inertial frames

Q. Find the MOI of four identical solid spheres each of mass $M$ and radius $R$ placed in a horizontal plane as shown in figure. Line $X{X}^{\prime }$ touches two spheres and passes through the diameter of the other two spheres.

1. $\frac{9}{10}M{R}^2$
2. $\frac{5}{18}M{R}^2$
3. $\frac{18}{5}M{R}^2$
4. $\frac{9}{5}M{R}^2$

Q. moment of inertia of trinagular lamina along its vertex , centroid, and bas

Q. A square plate of edge ${\frac{{}^{\prime }a}{2}}^{\prime }$ is cut from a uniform square plate of edge 'a' as shown in figure. Mass of square plate of edge 'a' is $M$. Find out the moment of inertia of the remaining square plate about an axis passing through 'O' (center of square plate of side 'a') and perpendicular to the plane of the plate.

1. $\frac{5}{192}M{a}^2$
2. $\frac{27}{64}M{a}^2$
3. $\frac{9}{64}M{a}^2$
4. $\frac{M{a}^2}{6}$

Q. Seven identical circular planar disks, each of mass $M$ and radius $R$ are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is :

1. $\frac{181}{2}M{R}^2$
2. $\frac{19}{2}M{R}^2$
3. $\frac{55}{2}M{R}^2$
4. $\frac{73}{2}M{R}^2$

Q. Necessary condition for the application of parallel axes theorem:
$I_A=I_B+M{d}^2$
where $A\text{and}B$ are the axes of rotation of body and $M$ is the mass of body.

1. Axis $B$ must pass through C.O.M of body
2. Axis $A$ must be parallel to axis $B$
3. $d$ must be shortest distance between axis $A$ and axis $B$
4. All of these

Q. In the figure given below, four identical circular rings of mass $10\text{kg}$ and radius $1\text{m}$ each, are lying in the same plane. The moment of inertia of the system about an axis through point $A$ and perpendicular to the plane of the rings is

1. $440{\text{kg-m}}^2$
2. $220{\text{kg-m}}^2$
3. $880{\text{kg-m}}^2$
4. $1000{\text{kg-m}}^2$

Q. A disc of mass $M$ and radius $R$ is attached to a rectangular plate of the same mass $M$, breadth $R$ and length $2R$ as shown in figure. The moment of inertia of the system about the axis $AB$ passing through the centre of the disc and on the plane is $I=\frac{1}{\alpha }\left(\frac{31}{3}M{R}^2\right)$. Then, the value of $\alpha$ is

Q. A thin square plate of side $3\text{m}$ has mass $5\text{kg}$. Find the moment of inertia about axis $AB$ as shown in figure.

1. $15{\text{kg-m}}^2$
2. $30{\text{kg-m}}^2$
3. $45{\text{kg-m}}^2$
4. $7.5{\text{kg-m}}^2$

Q. Three rods each of length L and mass M are placed along X, Y and Z-axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about Z axis is.

1. $\frac{2M{L}^2}{3}$
2. $\frac{4M{L}^2}{3}$
3. $\frac{5M{L}^2}{3}$
4. $\frac{7M{L}^2}{3}$

Q. A uniform rod of length $l$ is rotated about its end and it has a moment of inertia $\alpha kg{m}^2$. What is the moment of inertia of a rod about a point $\frac{l}{4}$ away from the center?

1. $\frac{7}{16}\alpha$
2. $\frac{5}{18}\alpha$
3. $\frac{3}{12}\alpha$
4. $\frac{4}{13}\alpha$