This set of Tricky Engineering Mechanics Questions and Answers focuses on “Mohr’s Circle for Moments of Inertia”.

1. Which of the following is the equation which we get for the graphical solution of the moment of inertia?

a)

b)

c)

d)

View Answer

Explanation: In the graphical method of solving the moment of inertia of the structures, we have the answer as the driven equation. Thus this equation is used so as to ease the calculations. This equation is derived from the equations of the product of area inertia. Thus the equation.

2. What is the radius of the Mohr circle of the structure given below?

a) 3.29

b) 0.29

c) 3.9

d) 2.9

View Answer

Explanation: In the above question, Ix, Iy and Ixy are meant to be calculated. This is because they are the derived quantity. It is dependent on the values of the structure which is constant. It means they are derived from constant values of the structure, thus they become a constant value.

3. The tendency of rotation of the body along with axis is also called ___________ As used for the construction of the Mohr circle.

a) Moment of inertia

b) Moment of couple

c) Torque

d) Force

View Answer

Explanation: The tendency of rotation of the body along with axis also called the torque. It is the moment of the force acting perpendicular to the direction of the axis of rotation. If the axis and the force are meeting at any point then there is no moment applied by the force.

4. The body is sometimes acted by two or three force members and we need to find the Mohr‘s circle for inertia for the same. The difference between the two and the three force members is:

a) The former is collinear and the latter is parallel

b) The former is parallel and the latter is perpendicular

c) The former is perpendicular and the latter is collinear

d) The former is acting on two points in the body while the latter is on three points

View Answer

Explanation: The definition of the two force member only defines that the forces are being acted on the two points on the body. So does is the definition of the three forces members. The points of action of the three forces are three.

5. Which of the following is the equation which we get for the graphical solution of the moment of inertia?

a) (Iv – a)^{2} + I^{2}uv = R^{2}

b) (Iu + a)^{2} + I^{2}uv = R^{2}

c) (Iv – a)^{2} + I^{2}uv = R^{2}

d) (Iv + a)^{2} + I^{2}uv = R^{2}

View Answer

Explanation: In the graphical method of solving the moment of inertia of the structures, we have the answer as the driven equation. Thus this equation is used so as to ease the calculations. This equation is derived from the equations of the product of area inertia. Thus the equation.

6. What are Ix, Iy and Ixy in the equation?

a) Variables

b) Constants

c) Alphanumeric

d) Gauss numbers

View Answer

Explanation: None.

7. Whenever the distributed loading acts perpendicular to an area its intensity varies __________ for the determination of the Mohr’s circle for inertia.

a) Linearly

b) Non-Linearly

c) Parabolically

d) Cubically

View Answer

Explanation: The load intensity is varying linearly in the structures. Thus the intensity is not varying parabolically nor is it cubically. It cannot be a vector also. Thus the intensity is linearly varied.

8. Given equation is wrong for the calculations of the moments.

a) False

b) True

View Answer

Explanation: The above equation is true for the calculation of the moments. , here Ix , Iy and Ixy are constants. This is because they are the derived quantity from the constants itself. This is the graphical method of solving the moment of inertia of the structures.

9. What is the Imax of the Mohr circle of the structure given below?

a) 7.54 x 109mm^{4}

b) 0.54 x 109mm^{4}

c) 7.4 x 109mm^{4}

d) 5.4 x 109mm^{4}

View Answer

Explanation: None.

10. What does the moment of the force measure in the calculation of the Mohr circle’s data for the moments of inertia?

a) The tendency of rotation of the body along with any axis

b) The moment of inertia of the body about any axis

c) The couple moment produce by the single force acting on the body

d) The total work is done on the body by the force

View Answer

Explanation: The moment of the force measures the tendency of the rotation of the body along any axis, whether it be the centroid axis of the body, or any of the outside axis. The couple moment is produced by two forces, not by a single force. The total work done is the dot product of force and distance not the cross. A use of Mohr circle can also help in determining the direction.

11. (Iu – a)^{2} + I^{2}uv = R^{2}; this equation is wrong for the calculations of the moments.

a) False

b) True

View Answer

Explanation: The above equation is true for the calculation of the moments. Here Iu and Iuv are not constants. This is because they are the derived quantity from the variables. This is the graphical method of solving the moment of inertia of the structures.

12. The Mohr’s circle for an area is helpful so as to________

a) Determine Minimum moments of inertia for an Area

b) Determine Maximum moments of inertia for a Line

c) Determine Minimum moments of inertia for a Volume

d) Determine Maximum moments of inertia for a Rectangle

View Answer

Explanation: The Mohr’s circle is important as to know what is the maximum and the minimum moment of inertia of an area. This data is required to design the structure of the body. This means that the designing of the body is majorly done by the help of the determination of the product of the moment of Inertia.

13. If the non-Uniform loading is of the type of parabola then for calculating the Mohr’s circle for the inertia for areas?

a) The net load will not be formed as all the forces will be cancelled

b) The net force will act the centre of the parabola

c) The net force will act on the base of the loading horizontally

d) The net force will act at the centroid of the parabola

View Answer

Explanation: The net force will act at the centroid of the parabola. Whether it be a parabola or the cubic curve the centroid is the only point at which the net force act. Force can’t be acted horizontally if the loading is vertical. Hence whatever be the shape of the loading, the centroid is the point of action of net force. Thus the use of centroid.

14. If any external force also is applied on the structure and we are determining the Mohr’s circle for the inertia then what should we consider?

a) The net force will act at the centroid of the structure only

b) The net load will not be formed as all the forces will be cancelled

c) The net force will act on the base of the loading horizontally

d) The net force will not to be considered, there would be a net force of the distribution, rest will be the external forces

View Answer

Explanation: The external forces are treated differently. They are not added by the force of the distributed loading. That is the force not only acts at the centroid always. It can be shifted also. Depending on the external forces. Thus the use of centroid or centre of mass.

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