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# Multiple choice question for engineering

## Set 1

1. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:
a) u = xcosθ + ysinθ
b) u = xcosθ – ysinθ
c) u = ycosθ + xsinθ
d) u = ycosθ – xsinθ

Answer: a [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

2. In the calculations of moments of inertia for an area about inclined axis we use the product of moment of inertia. It is the the sum of _____________ and _________________
a) Area and volume
b) Volume and linear distance
c) Moment of inertia at centroid and the product of the area and del dx and del dy
d) Moment of inertia at base and the product of the area and del dx and del dy

Answer: d [Reason:] The product of moment of inertia is required as 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.

3. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:
a) Iu = Ix cos2θ + Iysin2θ – 2Ixycosθsinθ
b) Iv = Ixcos2θ + Iysin2θ – 2Ixycosθsinθ
c) Iu = Ixcos2θ + Iysin2θ – 2Ixycosθsinθ
d) Iv = Ixcos2θ + Iysin2θ + 2Ixycosθsinθ

Answer: d [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

4. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:

Answer: a [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

5. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:
a) v = xcosθ + ysinθ
b) v = xcosθ – ysinθ
c) v = ycosθ + xsinθ
d) v = ycosθ – xsinθ

Answer: d [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

6. There is parallel axis theorem for the area, and it is can be used to determine the moment of inertia of an area about inclined axis.
a) True
b) False

Answer: b [Reason:] There is no perpendicular axis theorem for the area. In spite there is the theorem as parallel axis for any area. Thus we have the theorem which is used to add the two mutually perpendicular moment of inertias.

7. Determine the moment of inertia of the area about y-axis.

a) 0.273m2
b) 11m2
c) 0.141m2
d) 0.811m2

Answer: a [Reason:] Parallel axis for any area is used to add the two mutually perpendicular moment of inertias for areas. It gives a moment of inertia perpendicular to the surface of the body. That is the moment of inertia perpendicular to the surface in considerance.

8. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:

Answer: a [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

9. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:
a) Iu = Ixcos2θ + Iysin2θ – 2Ixycosθsinθ
b) Iv = Ixcos2θ + Iysin2θ – 2Ixycosθsinθ
c) Iu = Ixcos2θ + Iysin2θ – 2Ixycosθsinθ
d) Iv = Ixcos2θ – Iysin2θ + 2Ixycosθsinθ

Answer: a [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

10. Moment of Inertia about an inclined axis is the integration of the cube of the distance of the centroid and the del area along the whole area of the structure and after this calculations we multiply the moment of areas.
a) True
b) False

Answer: b [Reason:] The moment of inertia of the section is the integration of the square of the distance of the centroid and the del area along the whole area of the structure. This is having much significance in the various fields in the engineering sector. The main types are the ‘I’ section structures which are being much used.

11. Determine the moment of inertia of the area about x-axis.

a) 0.111m2
b) 11m2
c) 0.141m2
d) 0.811m2

Answer: a [Reason:] Parallel axis for any area is used to add the two mutually perpendicular moment of inertias for areas. It gives a moment of inertia perpendicular to the surface of the body. That is the moment of inertia perpendicular to the surface in considerance.

12. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:

Answer: a [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

13. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:

Answer: a [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

14. In the calculations of the moment of inertia of the area about an inclined axis, we have some transformation done. They are:
a) Iuv = Ixcosθsinθ – Iysinθcosθ + Ixy (cos2θ-sin2θ)
b) Iuv = Ixcosθsinθ + Iysinθcosθ – Ixy (cos2θ-sin2θ)
c) Iuv = Ixcosθsinθ – Iysinθcosθ – Ixy (cos2θ-sin2θ)
d) Iuv = Ixcosθsinθ + Iysinθcosθ + Ixy(cos2θ-sin2θ)

Answer: a [Reason:] In the moment of inertia calculations we see that the net force acts at the centroid of the loading body. That is if the loading system is in the form of the triangle then at the distance 2 by 3 of the base the net force of the loading will act. And the load will be half the area of the loading. Thus when there is the inclination of the axis, we use transformation.

15. If any external moment along with the force is applied on the structure and we are determining the moment of inertia for areas about inclined axis 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

Answer: d [Reason:] 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.

## Set 2

1. Which of the following is correct in bending moment diagram w.r.t the moment (M) of the force (F) acting on the body at a distance L from the axis of the rotation?
a) M=FLsinθ
b) M=FLcosθ
c) M=F.Lsinθ
d) M=FxLsinθ

Answer: a [Reason:] The moment of the force about the axis of rotation by the application of the force on the body is given by the cross product of both. If the force not perpendicular to the axis, and making angle θ then cosine form of angle is used. As usually used in the cross product.

2. What does the moment of the force measure in the bending moment diagram?
a) The tendency of rotation of the body along 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 done on the body by the force

Answer: a [Reason:] 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.

3. Determine the moment’s magnitude produce by the force as shown in the diagram, which tends to rotate the rod ORQP along QP.

a) 80.49 Nm
b) 72.12 Nm
c) -36.67 Nm
d) 36.67 Nm

Answer: a [Reason:] The use of the formula A.(rxF) gives the answer. In which A is 0.89i + 0.447j m. And the force is 300N, which is being applied at the end of the rod. Thus, after finding the equation of the axis and then replacing it in the equation shown above we get the answer. Actually, the main task is to know the axis equation in the vector form. Then get the magnitude of the moment.

4. The moment of the force in bending moment diagram is the product of the force and the perpendicular distance of the axis and the point of action of the force.
a) True
b) False

Answer: a [Reason:] The moment is the product of the force applied to the body and the perpendicular distance of the point of action of the force to the axis about which the body is being rotated. That is the moment is the cross product of the force and the distance between the axis and the point of action.

5. If any force is applied in the direction of the positive x-axis, and there are three different point in bending moment diagram on which the moment of this force is to be calculated. Then if these three points are on the positive side of the y-axis with varying distance, then what will be the direction of the moment caused by the force to the individual point?
a) Towards positive z-axis
b) Towards positive y-axis
c) Towards positive x-axis
d) Towards negative z-axis

Answer: a [Reason:] If you will apply he right hand rule on the system given then the right answer is the positive z-axis. Which is because the force is lying on the x-axis and is heading towards the positive infinity of the x-axis. And the points are in the positive y-axis. Apply the rule, and get the direction.

6. Determine the moment of the force F along the segment QP of the pipe assembly shown in the figure.

a) 110Nm
b) 100Nm
c) 500Nm
d) 510Nm

Answer: b [Reason:] The use of the formula A.(rxF) gives the answer. In which A is 0.6i + 0.8j m and the r is 0.5i + 0.5k. And the force is 300N, which is being applied at the end of the rod. Thus, after finding the equation of the axis and then replacing it in the equation shown above we get the answer. Actually, the main task is to know the axis equation in the vector form. Then get the magnitude of the moment.

7. Which of the following is true for bending moment diagram?
a) Total moment of various forces acting on the body is the vector sum of all moments
b) Total moment of various forces acting on the body is the algebraic sum of all moments
c) Total moment of various forces acting on the body is always zero
d) Total moment of various forces acting on the body is the vector sum of all moments which is perpendicular to each other forces

Answer: a [Reason:] The moment is the vector quantity. Thus the value of the total moment caused by various forces acting on the body is the vector sum of all the vectors. Also the moments are not perpendicular to each other, unless it is specified. Thus assumptions cant be taken for the direction of the moment.

8. If you are getting to know about the direction of the moment caused by the force applied on the body by using your wrist and curling it in the direction of the rotation then which of the following is not right for bending moment diagram?
a) The thumb represents the direction of the force
b) The thumb represents the direction of the moment
c) The fingers represents the direction of the force
d) The direction in which you curl your wrist is towards the direction of the distance from point of contact of force to the axis of rotation.

Answer: b [Reason:] The curled hand represents various thing. The direction of the moment axis is given by the thumb. The direction of the force is given by the fingers. As we place the fingers on the force and curl towards the rotational direction of the body about the axis.

9. If the rotation is clockwise in this page, suppose, then in which direction will the thumb project if you curl your hand in the same direction of the rotation for bending moment diagram?
a) It will point to the direction perpendicular to the plane of paper and towards you
b) It will point to the direction perpendicular to the plane of paper and away from you
c) It will point to the direction parallel to the plane of paper and towards right
d) It will point to the direction parallel to the plane of paper and towards left

Answer: b [Reason:] As the curling will give the direction perpendicular to the paper. But it does depend upon the rotation sense. In this example, the sense is clockwise. Thus the thumb goes into the paper. That is it goes away from the viewer. Thus the answer.

10. The tendency of rotation of the body along any axis in bending moment diagram is also called ___________
a) Moment of inertia
b) Moment of couple
c) Torque
d) Force

Answer: c [Reason:] The tendency of rotation of the body along any 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.

11. What does FLsinθ means/represents in bending moment diagram for the moment (M) of the force (F) acting on the body at a distance L from the axis of the rotation?
a) The direction vector of the moment
b) Unit vector of the moment vector
c) The magnitude of the moment caused by the force on the body
d) The perpendicular distance of the force from the axis of rotation

Answer: c [Reason:] The moment of the force about the axis of rotation by the application of the force on the body is given by the cross product of both. If the force not perpendicular to the axis, and making angle θ then cosine form of angle is used. Thus, FLsinθ represents the magnitude of the moment.

12. The moment axis, force and the perpendicular distance in the bending moment diagram is lying in____________.
a) Two planes perpendicular to each other
b) A single plane in the direction of the force
c) A single plane in the direction of the perpendicular distance
d) A single line in the direction of the force

Answer: a [Reason:] The moment axis, force and the perpendicular distance is lying in the three dimensional Cartesian. It doesn’t lye on the single plane. It also doesn’t lye in a single line. Nor in the direction of the force. Thus they all lye in the planes which are perpendicular to each other.

13. If a force applied at any point in its line of action and is still creating the same moment about any fixed point say P, then the force is said to be sliding vector. What is the name of this property in bending moment diagram?
a) Associative property
b) Distributive property
c) Negative associative property
d) Principle transmissibility of the force

Answer: d [Reason:] If a force applied at any point in its line of action and is still creating the same moment about any fixed point say P, then the force is said to be sliding vector. This is because the moment of the force which is acting on its line of axis at the point P is same throughout. This is known as the principle transmissibility of the force.

14. The basic way of getting the direction of the moment caused by the force in bending moment diagram is:
a) The use of left hand rule with thumb giving the direction of moment
b) The use of right hand rule with thumb giving the direction of moment
c) The use of right hand rule with forefinger giving the direction of moment
d) The use of left hand rule with forefinger giving the direction of moment

Answer: b [Reason:] The basic way of doing so is to use right hand rule and not the left hand rule. The direction of the moment axis is given by the thumb. The direction of the force is given by the fingers. As we place the fingers on the force and curl towards the rotational direction of the body about the axis.

15. If a force applied at any point in its line of action and is still creating the same moment about any fixed point say P, then the force in bending moment diagram is said to be______________
a) Couple
b) Sliding vector
c) Slider couple
d) Couple slider

Answer: b [Reason:] If a force applied at any point in its line of action and is still creating the same moment about any fixed point say P, then the force is said to be sliding vector. This is because the moment of the force which is acting on its line of axis at the point P is same throughout. Whatever be the direction of the distance.

## Set 3

1. Flexible cable with chains combine ___________ with lightness and often are used in structures for support.
a) Strength
b) Mass
c) Volume
d) Density

Answer: a [Reason:] The chains with the cables are used to support the structures. They ae there for the transfer of the loading from one point to another point. This means that the cables not only provides strength to the structure but also sufficiently transfers the loads that are being added to it.

2. In the support system of the bridges and trolley wheel ____________ form the main loading carrying element in the structure.
a) Cable
b) Beams
c) Pillars
d) Cement mortar

Answer: a [Reason:] The cable is a support system which is used to transfer the loadings in the different structures. The main motto is to make the structure stable. This is probably done with the help of making the distribution of the load which is being given to the structures equally by the help of the cables.

3. The force on the cables is not neglected in the calculations of the load distribution.
a) False
b) True

Answer: a [Reason:] The cable is a support system which is used to transfer the loadings in the different structures. The main motto is to make the structure stable. In calculation the self-weight of the cable is neglected and the load is calculated. The forces are acting in the vertically downward direction.

4. The cable weight become significant in the calculations of the loadings when the cables are used in the transmission lines and guys for radio antennas.
a) False
b) True

Answer: b [Reason:] The cable is a support system which is used to transfer the loadings in the different structures. The main motto is to make the structure stable. But in the calculations of the loadings when the cables are used in the transmission lines and guys for antennas the self-weight of the cable is not neglected and the load is calculated.

5. The assumptions for the calculations are done for the cables. In that one of the assumption is that the cable is ___________
a) Extensible
b) Non-flexible
c) Flexible
d) Static

Answer: c [Reason:] The assumptions are done so as to make the calculations easy. Though the assumptions make the small errors to not count over the big dat. But still if the assumptions are made then the calculations are easy. Thus the assumption taken as the cable is perfectly flexible.

6. The assumptions for the calculations are done for the cables. In that one of the assumption is that the cable is flexible and the other is that the cable is ___________
a) Extensible
b) Non-flexible
c) Inextensible
d) Static

Answer: c [Reason:] The assumptions are done so as to make the calculations easy. Though the assumptions make the small errors to not count over the big dat. But still if the assumptions are made then the calculations are easy. Thus the assumption taken as the cable is inextensible.

7. Determine the force in the section QR as shown in the figure.

a) 10.2KN
b) 12.6KN
c) 3.6KN
d) 11.6KN

Answer: a [Reason:] The various points in the cables are facing constant forces. The forces are tensile forces. This is because as the cables are subjected to loadings the loads tends to stretch the cables in the direction parallel to its round area region. Thus the points face tensile forces which are parallel to the cable length.

8. Due to which property the cable, it offers no resistance to bending?
a) Extensible property
b) Non-flexible property
c) Flexibility property
d) Static property

Answer: c [Reason:] Due to the flexibility property the cable, it offers no resistance to bending. As the bending is seen in the beams and all the solid structures. Thus the bending moment produced in the cables are not affecting the cables much. Thus no affect by bending, i.e. no resistance to bending.

9. The tensile force acting on the cable is in which direction w.r.t the cable?
a) Perpendicular
b) Parallel
c) Tangential
d) At an angle of 2 radians

Answer: c [Reason:] Due to the flexibility property the cable, it offers no resistance to bending. As the bending is seen in the beams and all the solid structures. Thus the bending moment produced in the cables are not affecting the cables much. So the tensile force which is being produced is acting in the tangential direction to the points of the cable along its lengths.

10. Being inextensible the cable has ___________ length.
a) Infinite
b) Zero
c) Average to zero
d) Constant

Answer: d [Reason:] The assumption that the cables are inextensible the main fact that comes out is that the cable length is constant throughout. Thus in the calculations also the fact that the length is constant makes a huge time saving tool. Thus the length of the cables are to be assumed constant if the assumption is taken as they are inextensible.

11. The loading in the cable doesn’t changes the ___________ of the cables.
a) Geometry
b) Colour
c) Bending moment
d) Point at which the shear stress is zero

Answer: a [Reason:] The loading in the cables doesn’t affect the geometry of the cables. This is because of the assumptions which we have taken. The first one that the cables are perfectly elastic. And the second one that the cables are inextensible.

12. Cable takes a shape of a ____________ when is subjected to loadings.
a) Helix
b) Line
c) Spring
d) Complex figure

Answer: b [Reason:] The cable takes the shape of straight line when subjected to the loadings. As the loadings are straight, acting vertically downwards, they stretch the cables and then make them come in the shape of the straight line. Thus the loadings make the cables come in the straight line.

13. The various points in the cable is facing a ____________ tensile force.
a) Constant
b) Variable
c) Insufficient
d) Non

Answer: a [Reason:] The various points in the cables are facing constant forces. The forces are tensile forces. This is because as the cables are subjected to loadings the loads tends to stretch the cables in the direction parallel to its round area region. Thus the points face tensile forces which are parallel to the cable length.

14. If the unknown variables in the calculations are more than the known quantities, then the number of equations required to solve all the unknown variables are?
a) Infinite
b) Finite
c) Not possible
d) Question fault

Answer: b [Reason:] Whatever be the calculation involved, the unknown variables will be ultimately come out from the equations. The proper use of the known quantities and the multiuse of various calculation techniques will ultimately give up the results. Thus whether it may be the case of the cables or the beams the equations if applied properly will result in the determination of the unknowns.

15. Determine the force in the section PQ as shown in the figure.

a) 13.6KN
b) 12.6KN
c) 3.6KN
d) 11.6KN

Answer: a [Reason:] The various points in the cables are facing constant forces. The forces are tensile forces. This is because as the cables are subjected to loadings the loads tends to stretch the cables in the direction parallel to its round area region. Thus the points face tensile forces which are parallel to the cable length.

## Set 4

1. The determination of the internal loading in the different structures is usually done so as to___________
a) Break the structure
b) Know the length
c) Know the diameter
d) Design the structure

Answer: d [Reason:] The determination of the internal forces in the structure is done so as to design the structure as in the application purpose the structure will be subjected to many loads. This will help us to make the beam properly. And also this will ensure that the structure will not break after the loading is done on them. For this another method is the distribution load method.

2. Determine the moment generated at R.

a) 18.75KNm
b) 8.75KNm
c) 1.75KNm
d) 175KNm

Answer: a [Reason:] The loading acting upward is considered to be positive. This is done as to decrease the time used for the calculations. If the method of sections is being applied at the complex sections for the determination of the unknown forces, much time is required for it. Thus the main motto is to make the calculations easy and make the less use of time.

3. Choose the correct one.
a) In a coplanar system the moment of the force is chose about a point instead of axis
b) In a coplanar system the moment of the force is chose about an axis instead of a point
c) In a 3D system the moment of the force is chose about a point instead of axis
d) In a 3D system the moment of the force is chose about an axis which is perpendicular ot the direction of the force

Answer: a [Reason:] The coplanar system means the consideration is with the 2D only. No 3D. Thus if there is any moment needed to be considered we need to take it along the point and not along the axis. But talking about the axis, there might be no axis in the 2D, as it is only in the 3D.

4. The slope of the shear diagram of the different structure is equal to__________
a) Rotational moment
b) Bending moment
c) Total weight

Answer: d [Reason:] After the application of the force equation of equilibrium to the segment of the structure, we have the above result. This is done on the very small part of the structure. That is the minimal section of the beam is to be considered and then the application of the equilibrium equations are done so as to calculate the final result.

5. Free body diagrams doesn’t play any role in making the calculations on the conditions of the resultants of the body.
a) True
b) False

Answer: b [Reason:] The free body diagrams does play an important role in the formation of the conditions of the resultants of the rigid body. As the net forces are zero, the fbd helps us to take the measure of the same. That is to see whether the summation is really zero or not.

6. The simplification of the forces on the axis is done as __________
a) A particular system of rule is followed
b) No simplification of the forces is possible
c) The forces are already simplified and don’t need simplification
d) The forces are very tentative quantity on terms of simplification and hence no simplification possible

Answer: a [Reason:] A particular system of the rules is followed that is if the upward direction is taken as positive then the downward direction is taken as negative. This is same as done with the couple in the 2D. That is the forces can be easily simplified. If taken in the vector form then the task is even easier.

7. Determine the shear force of the beam shown.

a) 450N
b) 50N
c) 40N
d) 45N

Answer: a [Reason:] The loading acting upward is considered to be positive. This is done as to decrease the time used for the calculations. If the method of sections is being applied at the complex sections for the determination of the unknown forces, much time is required for it. Thus the main motto is to make the calculations easy and make the less use of time.

8. The net forces of acting on the body needs to be zero. This is also applicable for the simply supported structures. This means that the support reaction are also counted in making the net force zero.
a) True
b) False

Answer: a [Reason:] The support reactions of the beam is also counted in the making of the forces zero. As far as the net force is concerned the support reaction does affect the conditions for the equilibrium of the body. Hence one needs to take care of the support reactions of the structures too.

9. What does the Newton’s third law states?
a) The rate of change of momentum is equal to the force applied
b) For every reaction there is an opposite reaction
c) The body is tend to be rotated if the force is applied tangentially
d) The body is rest until a force is applied

Answer: b [Reason:] The requirement of the third law is important in the determination of the resultants of the body. Specially the rigid bodies. The rigid body particles are in the equilibrium and are thus facing the forces and to be in the equilibrium they also react and apply the opposite force and thus the third law of newton.

10. The ___________ forces do not cause the rotation.
a) Non-concurrent
b) Concurrent
c) Parallel
d) Non-Parallel

Answer: b [Reason:] The concurrent forces are the which are somewhere touching the axis of rotation. If any of the force is touching that axis, that force is not considered, or is insufficient to cause a rotation. If a force is concurrent then the perpendicular distance of the force from the line of axis is zero, thus no rotation. As we know rotation is caused by moment.

11. Which of the following is correct?
a) The application of the conditions of the equilibrium of the body is valid only if the forces are collinear
b) The application of the conditions of the equilibrium of the body is valid only if the forces are parallel
c) The application of the conditions of the equilibrium of the body is valid only if the forces are perpendicular
d) The application of the conditions of the equilibrium of the body is valid throughout

Answer: d [Reason:] The application of the conditions of the equilibrium of the body is valid throughout. This means that the conditions are irrespective of the types of forces. The conditions are the basic rules that defines the equilibrium of the body and thus are applicable in any type of forces of the real axis.

12. For the conditions of the equilibrium of the body, i.e. the rigid body only the external forces defines the equilibrium. And the support reactions only cancels out the rotation part of the body.
a) The first part of the statement is false and other part is true
b) The first part of the statement is false and other part is false too
c) The first part of the statement is true and other part is false
d) The first part of the statement is true and other part is true too

Answer: c [Reason:] The application of the support reaction forces does affect the conditions of the equilibrium of the body. Not only the external but the support reaction forces that are developed by the sake of external forces does develop a tending effect on the equilibrium of the body. Thus the support reaction forces also cancels the external forces.

13. The simplification of the couple for getting the resultant is done on the basis of the ___________
a) The clockwise of the anti-clockwise rotation sign convention
b) The simplification is not possible
c) The couple is a vector and thus can’t be simplified
d) The couple is a scalar and can’t be simplified

Answer: a [Reason:] The couple is simplified by taking the direction of the rotation of the body as positive or negative. That is if the clockwise direction is positive then the anti-clockwise direction is taken as negative. If the couple is a vector it can be easily simplified by taking the components.

14. If the supports are properly aligned then the reaction forces developed are adequate to support the body.
a) Statement is true only in 2D
b) Statement is true only in 3D
c) Statement is true throughout
d) Statement is true only in 1D

Answer: c [Reason:] This is the basic nature observed during the experiments on the beams an all the support system. The dimension doesn’t affect the equilibrium conditions. The main motto is to achieve the equilibrium. It is achieved by equating the net force equal to zero.

15. The moment is the cross product of which two vectors?

Answer: b [Reason:] The cross product needs to take in the proper sequence. If not taken then the answer is just the opposite of the true answer. That’s why, the answer is not the Force and Radius vectors, but the Radius and Force vectors. Because the moment has its direction, as many of the cross products have, and thus precaution needs to be taken.

## Set 5

1. In right handed coordinate system which axis is considered to be positive?
a) Thumb is z-axis, fingers curled from x-axis to y-axis
b) Thumb is x-axis, fingers curled from z-axis to y-axis
c) Thumb is y-axis, fingers curled from x-axis to z-axis
d) Thumb is z-axis, fingers curled from y-axis to x-axis

Answer: a [Reason:] As right handed coordinate system means that you are curling your fingers from positive x-axis towards y-axis and the thumb which is projected is pointed to the positive z-axis. Thus visualizing the same and knowing the basic members of axis will not create much problem.

2. If A is any vector with Ai + Bj + Ck then what is the y-axis component of the vector?
a) B units
b) A units
c) C units
d) Square root of sum of squares of the three, i.e. A, B and C

Answer: a [Reason:] As the given vector is shown in the Cartesian system, the number with “j” is the Y-axis component of the given vector. With the numbers with “i” representing components of x-axis and “k” representing the z axis respectively.

3. If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by?
a) Xi + Yj + Zk
b) Yi + Xj + Zk
c) Zi + Yj + Xk
d) Zi + Xj + Yk

Answer: d [Reason:] It is given that x, y and z-axis components are Z, X and Y respectively. Thus, just by placing the right coordinates we get option d to be correct. Here just the interchange of the axis’s representor with their respective axis is creating confusion. Which must be figured out.

4. Which statement is right for force vector F = Ai + Bj + Ck?
a) In rectangular components representation of any vector we have vector F = Ai + Bj + Ck
b) In rectangular components representation of any vector we have vector F = Ax + By + Cz
c) In rectangular components representation of any vector we have vector F = Fx + Fy + Fz
d) In rectangular components representation of any vector we have vector F = Fi + Fj + Fk

Answer: c [Reason:] As given the vector is F = Ai + Bj + Ck, this implies that the x ,y and z-axis components of this vector is A, B and C respectively. But, in rectangular components representation of any vector, the vector is written as F = Fx + Fy + Fz.

5. What is the magnitude of the Cartesian vector having the x, y and z axis components to be A, B and C?
a) Square root of the squares each A, B and C
b) Square of the squares each A, B and C
c) Cube root of the squares each A, B and C
d) Cube of the squares each A, B and C

Answer: a [Reason:] The magnitude of a Cartesian vector having the x, y and z axis components to be A, B and C is always the square root of the squares each A, B and C. This comes from the distance formula between two points in the Cartesian plane. That is the square root of the subtraction of final and initial point of line.

6. What is cosα for force vector F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis respectively) ?
a) B/F
b) C/F
c) A/F
d) 1

Answer: c [Reason:] The cosine component of the vector is defined as the ratio of the x-axis component to the magnitude of the vector, i.e. F in this case. Likewise the sine component is the ratio of y-axis component to the magnitude of the vector.

7. What is the sum of squares of the cosine angles made by the force vector with the coordinate axis?
a) 1
b) ½
c) 2
d) 3

Answer: a [Reason:] The sum of the squares of the cosines of the vector will give you the squares of the components in the numerator, and the vector’s magnitude’s square in the denominator. But the numerator sum is equal to the vector’s magnitude’s square. Thus, the answer = 1.

8. What is x-axis component of the force vector Ai + Bj +Ck with magnitude equal to F?
a) B
b) C
c) Fcosα
d) Fcosβ

Answer: c [Reason:] As we know that the cosα is the ratio of the x-axis component to the magnitude of the vector. Thus the x-axis components is Fcosα, F, the magnitude in the case. Likely if we want to take the y-axis component we would try to do the same with the sine component.

9. We can add the force vectors directly. But with dividing each by it’s magnitude first. (True/False)
a) True
b) False

Answer: b [Reason:] False, because if you will divide the magnitude of the vector to itself than the resulting would be the unit vector. Which is just giving you the direction of the vector, not the vector itself. This means unit vector has direction same as it’s respective vector but having magnitude equal to one.

10. For a vector F, Fcosβ is equal to zero. What does this refer?
a) X-axis component is zero
b) Y-axis component is zero
c) Z-axis component is zero
d) β = 180˚

Answer: b [Reason:] As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus y-axis component is zero, or β = 90˚. And thus if the angle is giving component to be zero this means the vector in that particular axis is perpendicular to that axis.

11. Which statement is correct about the vector F?
a) F= Fcos β + Fcos α + Fcosγ
b) F= Fsin β + Fcos α + Fcosγ
c) F= Fcos β + Fsin α + Fcosγ
d) F= Fcos β + Fcos α + Fsinγ

Answer: a [Reason:] As we know the α, β and γ are the angles made by the x, y and z-axis respectively. Thus, is the magnitude of the vector is F, the F= Fcos β + Fcos α + Fcosγ. Which means the force is the resultant of all its axis’ components.

12. Which is true?
a) ∑F = ∑Fx + ∑Fy + ∑Fz
b) ∑F = -(∑Fx + ∑Fy + ∑Fz)
c) ∑F = ∑Fxi + ∑Fyj + ∑Fzk
d) ∑F = -(∑Fxi+ ∑Fyj + ∑Fzk)

Answer: c [Reason:] The total of two or more forces is equal to the sum of their respective axis’s components. That is the resultant adds up all the components of the forces in their respective axis, whether it may be x, y or z axis.

13. Find the angle α, for the vector making an angle by y and z axis as 60˚ and 45˚ respectively. It makes an angle of α with x-axis. The magnitude of the force is 200N.
a) 60˚
b) 120˚
c) 45˚
d) 90˚

Answer: a [Reason:] When you will resolve the vector in its x, y and z-axis components, you will get an equation containing cosα. After getting the α correctly, you need to directly put that value in the previous equation of components. α = 60˚. As 120˚ will give negative component. Just try to resolve the vector in its components.

14. What is the magnitude of the resultant force when F1 = 60j + 80k and F2 = 50i – 100j + 100k?

a) 188 unit
b) 191 unit
c) 181 unit
d) 120 unit