Moment of Inertia of a Rod

Q. A rod is lying along x-axis with its left extreme at origin as shown in figure. The density of the rod increases by the rate, $\frac{dm}{dx}=5x\frac{kg}{m}$. The length of the rod is 2m. What will be its rotational inertia about Z axis?

1. $\frac{10}{3}kg-m^2$
2. $\frac{20}{3}kg-m^2$
3. $10kg-m^2$
4. $20kg-m^2$

Q. A rod of length 4m is rotated about an axis perpendicular to the rod and passing through a point 1 m from one of its end as shown in figure. The rod has a uniform mass density and has a total mass of 10 kg. What will be its moment of Inertia about this axis?

1. $\frac{70}{3}Kg-m^2$
2. $\frac{35}{3}Kg-m^2$
3. $\frac{70}{6}Kg-m^2$
4. $\frac{35}{6}Kg-m^2$

Q. A rod of uniform mass 2kg has a length of 5m. What will be its moment of inertia about a line perpendicular to the rod and passing through its middle point?

1. $25kg-m^2$
2. $\frac{25}{6}kg-m^2$
3. $\frac{15}{7}kg-m^2$
4. $\frac{25}{3}kg-m^2$

Q.

Two masses, A and B, are fixed at both the ends of a light rod as shown in figure. There are two axis 00' and AA' about which the rod can be rotated. In which of the case the rotational inertia of the system will be more?

1. 00'

2. It will be the same about both axis.

3. None of these

4. AB

Q. A rod is of length 2 m and mass 1kg. What will be its moment of inertia about an axis perpendicular to its length and passing through one of its end?

1. $\frac{4}{3}kg-m^2$
2. $\frac{2}{3}kg-m^2$
3. $\frac{3}{4}kg-m^2$
4. $\frac{1}{3}kg-m^2$

Q.

Find the moment of inertia of a uniform rod of mass $M$ and length $L$, about $OA$ {$PQ$ makes an angle of ${30}^{\circ }$ with $OA$ as shown in figure}.

1. 

2. 

3. 

4. 

Q. A rod is of length 2 m and of mass 1 kg. Moment of inertia about an axis perpendicular to its length and passing through one of its end is

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

Q. Two conical portions each of height 2R are removed from a cylinder of length 4R and radius R as shown in figure. If density of the material is $\mathrm{\rho ,}$ then moment of inertia of given system about the axis of cylinder is

1. $\frac{8}{5}\rho \pi R^5$
2. $\frac{4}{5}\rho \pi R^5$
3. $\frac{2}{3}\rho \pi R^5$
4. $\frac{5}{3}\rho \pi R^5$

Q. Four identical rods are joined end to end to form a square. The mass of each rod is $M$. The moment of inertia of the square about the central line $y{y}^{\prime }$ as shown in figure is

1. $\frac{M{l}^2}{3}$
2. $\frac{M{l}^2}{6}$
3. none of these
4. $\frac{M{l}^2}{4}$

Q. The mass density of the material of a $\text{T}$ joint is $2\text{kg/m}$. The dimensions of this joint are shown in the figure.


What is the approximate moment of inertia ($\text{MI}$) of the $\text{T}$ joint about an axis passing through their common joining point and perpendicular to the plane of structure?

1. $362{\text{kg-m}}^2$
2. $426{\text{kg.m}}^2$
3. $120{\text{kg-m}}^2$
4. $240{\text{kg-m}}^2$