Parallel Axis Theorem

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 (in ${\text{kg m}}^2$) of the system about an axis through point $A$ and perpendicular to the plane of the rings is

Q.

Two thin discs each of mass 4.0 kg and radius 0.4 m are attached as shown in figure to form a rigid body. What is the rotational inertia of this body about an axis perpendicular to the plane of disc $B$ and passing through its center?

1. 

2. 

3. 3.2kg - m²

4. 

Q. Four thin rods of same mass 'M' and same length 'l', form a square as shown in the figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is

1. 
2. 
3. 
4. 

Q. The moment of inertia of a rod of length 'l' about an axis passing through its centre of mass and perpendicular to rod is 'I'. The moment of inertia of hexagonal shape formed by six such rods, about an axis passing through its centre of mass and perpendicular to its plane will be

1. 
2. 
3. 
4. 

Q.

Two identical spheres each of mass 1.20 kg and radius 10.0 cm are fixed at the ends of a light rod so that the separation between the centres is 50.0 cm. Find the moment of intertia of the system about an axis perpendicular to the rod passing through its middle point.

1. 0.19kg - m²

2. 190kg - m²

3. 0.16kg - m²

4. 160kg - m²

Q.

A thin wire of length L and uniform linear mass density $\rho$ Is bent into a circular loop with centre at 0 as shown in the figure. The moment of inertia of the loop about the axis XX’ is

1. $\frac{\rho L^3}{8{\pi }^2}$

2. $\frac{\rho L^3}{16{\pi }^2}$

3. $\frac{5\rho L^3}{16{\pi }^2}$

4. $\frac{3\rho L^3}{8{\pi }^2}$

Q. Two thin discs each of mass 4.0 kg and radius 0.4 m are attached as shown in figure to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc $B$ and passing through its center is.

1. $1.6kg{m}^2$
2. $3.2kg{m}^2$
3. $6.4kg{m}^2$
4. $0.8kg{m}^2$

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. The radius of gyration of a uniform rod of length $l$ about an axis passing through a point $l/4$ away from the center of the rod, and perpendicular to it, is

1. $\frac{1}{4}l$
2. $\frac{1}{8}l$
3. $\sqrt{\frac{7}{48}}l$
4. $\sqrt{\frac{3}{8}}l$

Q. From a disc of radius $R$ and 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. $\frac{13M{R}^2}{32}$
2. $\frac{11M{R}^2}{32}$
3. $\frac{9M{R}^2}{32}$
4. $\frac{15M{R}^2}{32}$