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# Multiple choice question for engineering

## Set 1

1. The main condition for the rigid body is that the distance between various particles of the body does change.
a) True
b) False

Answer: The main condition for the rigid body is that the distance between various particles of the body does not change. If the distance does change the body is not to be called as rigid. Thus the fix distance of the particles is very much required for the equilibrium of the rigid body.

2. The shown here has a mass of 100kg. What is missing here in the diagram?

a) The weight of the body is not shown
b) The moment of the force is not shown
c) The body cant be held like this
d) The body diagonal is not shown

Answer: a Answer: The main condition for the rigid body is that the distance between various particles of the body does not change. If the distance does change the body is not to be called as rigid. Thus the fix distance of the particles is very much required for the equilibrium of the rigid body.

3. 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 equilibrium 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.

4. Determine the horizontal components of the reaction on the beam caused by the pin at P. The force 60N is multiplied by 10 and then is applied.

a) 424N
b) 24N
c) 44N
d) 441N

Answer: a [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to be equal to zero. The basic need of the forces to make the body in equilibrium.

5. For equilibrium the net force acting on the body is zero.
a) True
b) False

Answer: a [Reason:] The equilibrium is only attained if the net force on the body tends to be equal to zero. Thus the forces cancels out. If this happens there is no motion of the body along any direction and hence the body is said to be in equilibrium. The body here is a rigid body.

6. For equilibrium the net moment acting on the body by various forces is zero.
a) True
b) False

Answer: a [Reason:] The equilibrium is only attained if the net moment on the body tends to be equal to zero. Thus the moments caused by different forces cancels out. If this happens there is no motion of the body along any direction and hence the body is said to be in equilibrium. The body here is a rigid body.

7. Determine the vertical components of the reaction on the beam caused by the pin at Q. The force 60N is multiplied by 10 and then is applied.

a) 319N
b) 445N
c) 45N
d) 40N

Answer: a [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to be equal to zero. The basic need of the forces to make the body in equilibrium.

8. The net moment of the body is zero that means the distance between the force and the rotational axis is zero.
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 net moment of the body is zero that doesn’t means that the distance between the force and the rotational axis is zero. This means moments caused by different forces cancels out. If this happens there is no motion of the body along any direction and hence the body is said to be in equilibrium.

9. Determine the horizontal components of the reaction on the beam caused by the roller at P.

a) 536N
b) 536cos30N
c) 536sin30N
d) 536tan30N

Answer: c [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to be equal to zero. The basic need of the forces to make the body in equilibrium.

10. The net force of the body is zero that means the force are not being applied to the body at all and hence the body is in equilibrium.
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 net force of the body is zero that doesn’t means that the force are not being applied to the body at all and hence the body is in equilibrium. The equilibrium is only attained if the net force on the body tends to be equal to zero. Thus the forces cancels out. If this happens there is no motion of the body along any direction and hence the body is said to be in equilibrium.

11. Which of the following is correct?
a) The application of the conditions of the equilibrium of the body is valid only in the 2D
b) The application of the conditions of the equilibrium of the body is valid only in the 3D
c) The application of the conditions of the equilibrium of the body is valid only in the 1D
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 dimensions. The conditions are the basic rules that defines the equilibrium of the body and thus are applicable in any dimension of the real axis.

12. Determine the vertical components of the reaction on the beam caused by the roller at P.

a) 536N
b) 536cos30N
c) 536sin30N
d) 536tan30N

Answer: b [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to be equal to zero. The basic need of the forces to make the body in equilibrium.

13. For the conditions of the equilibrium of the body, i.e. the rigid body only the external forces defines the equilibrium. Because the internal forces cancels out so not to be considered.
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 internal forces does affect the conditions of the equilibrium of the body. Not only the external but the internal forces that are developed by the sake of external forces does develop a tending effect on the equilibrium of the body. Thus the internal forces doesn’t cancels out.

14. Which of the following needs to zero for the perfect equilibrium?
a) ∑F=0, ∑M=0 and ∑θ = 0
b) ∑F=0, ∑M≠0 and ∑θ = 0
c) ∑F≠0, ∑M=0 and ∑θ = 0
d) ∑F=0, ∑M=0 and ∑θ≠0

Answer: d [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to be equal to zero. The basic need of the forces to make the body in equilibrium.

15. Determine the vertical components of the reaction on the beam caused by the pin at P. The force 60N is multiplied by 10 and then is applied.

a) 405N
b) 445N
c) 45N
d) 40N

Answer: a [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to be equal to zero. The basic need of the forces to make the body in equilibrium.

## Set 2

1. If a block moves from a height h above the ground then the work done is given by_______

Answer: a [Reason:] The potential energy is converted into the work done. Thus is the block moves from the height h to the ground, the work done is given by . Negative because the work done is in the opposite direction of the motion of the body.

2. If any external conservative force also is applied on the distributed loading then?
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.

3. Find the tension in the cable AC.

a) 23.6N
b) 55N
c) 89N
d) -29N

Answer: a [Reason:] First represent the forces in their vector form. Then equate the net sum of the forces in the x, y and z directions to be zero. You will get FB = FC and 2(.848) = 40N. This gives the answer as 23.6N.

4. What is the sum of squares of the cosine angles made by the conservative 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.

5. ____________ is the phenomena that resist the movement of the two surfaces in contact. This phenomena is also having its scope in the work and the conservative nature of the force.
a) Friction
b) Motion
c) Circular movement
d) Rotation

Answer: a [Reason:] The friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. The two surfaces are in contact and the friction applies at that surface only, resisting the motion of the surface.

6. In the explanation of the theory of friction over which conservative forces were acted upon, the block used have an assumption. That is the upper portion of the block is considered to be rigid.
a) True
b) False

Answer: b [Reason:] The block used to explain the theory of friction is placed on a deformable surface. As we know that the theory of friction says that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. Thus to show the same, experiments are done over a non-rigid/deformable surface which is having a rigid shape.

7. Work done by a spring to a body from moving it from x1 to x2 distance is given by _________

Answer: a [Reason:] The potential energy is converted into the work done. Thus is the block moves from the distance x2 to x1, the work done is given by . Negative because the work done is in the opposite direction of the motion of the body.

8. Which statement is right for conservative 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.

9. For equilibrium the net moment acting on the body by various conservative forces is zero.
a) True
b) False

Answer: a [Reason:] The equilibrium is only attained if the net moment on the body tends to be equal to zero. Thus the moments caused by different forces cancels out. If this happens there is no motion of the body along any direction and hence the body is said to be in equilibrium. The body here is a rigid body.

10. Determine the horizontal components of the reaction on the beam caused by the pin at Q. The force 60N is multiplied by 10 and then is applied.

a) 0N
b) 445N
c) 45N
d) 40N

Answer: a [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to.

11. The conservative frictional force always acts ____________ to the surface of the application of the friction.
a) Tangential
b) Perpendicular
c) Parallel
d) Normal

Answer: a [Reason:] The friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. This friction is applied tangentially to the surfaces in contact. Thus the main thing is that the forces on both of the surfaces act tangential to each other.

12. What does the Newton’s third law states for the conservative forces?
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 equilibrium 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.It is same for all the methods.

13. We use sometimes the measures to know the direction of moment in the calculations of the moments caused by the conservative forces. Which one is right about it(consider the mentioned axis 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.

14. For the conditions of the equilibrium of the body, i.e. the rigid body only the external conservative forces defines the equilibrium. Because the internal conservative forces cancels out so not to be considered.
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 internal forces does affect the conditions of the equilibrium of the body. Not only the external but the internal forces that are developed by the sake of external forces does develop a tending effect on the equilibrium of the body. Thus the internal forces doesn’t cancels out.

15. Which statement is correct about the vector F in the showing the conservative nature of the forces?
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.

## Set 3

1. To satisfy the conditions of the equilibrium, the must not only be having a net force zero, but also be properly held or constrained on its supports.
a) True
b) False

Answer: a [Reason:] To satisfy the conditions of the equilibrium, the must not only be having a net force zero, but also be properly held or constrained on its supports. The more the stable are the supports the more the stable is the equilibrium, that is the more easily is the equilibrium is achived.

2. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the vertical reaction at the support P.

a) -217N
b) 80N
c) 700N
d) -250N

Answer: a [Reason:] As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.

3. What is redundant support?
a) The supports consisting of hinge and a roller
b) The supports consisting of hinge only
c) The supports consisting of roller only
d) The supports more than necessary to hold the structure

Answer: d [Reason:] The supports if are more than the supports required to hold the structure are termed as the reductant supports. It becomes statically indeterminate. This not only creates a problem in achieving the equilibrium but also affects the calculation of the equilibrium.

4. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the horizontal reaction at the support P.

a) 0N
b) 80N
c) 200N
d) 100N

Answer: a [Reason:] As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.

5. Statically indeterminacy means?
a) There will be less equations available for equilibrium than the unknown loadings
b) There will be more equations available for equilibrium than the unknown loadings
c) There will be equal equations available for equilibrium as the unknown loadings
d) The support reactions are opposite to each other

Answer: a [Reason:] Statically indeterminacy is the condition when less equations are available for equilibrium than the unknown loadings. This not only creates a problem in achieving the equilibrium but also affects the calculation of the equilibrium. Thus this is the stuff which one needs to prevent from happening.

6. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the horizontal reaction at the support R.

a) 0N
b) 30N
c) 20N
d) 10N

Answer: a [Reason:] As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.

7. The additional equations invented in the statically indeterminacy condition is solved by __________
a) Deformation conditions at the point of supports
b) Rotational equations
c) Translation equations
d) Linear rotation equations

Answer: a [Reason:] The additional equations invented in the statically indeterminacy condition is solved by deformation conditions at the point of supports. This are the conditions which are based on the physical and the chemical properties of the body. A different study for this is done in mechanics of material.

8. The generation of equal equations available for equilibrium as the unknown loadings always guarantees the stability of the body.
a) True
b) False

Answer: b [Reason:] The generation of equal equations available for equilibrium as the unknown loadings doesn’t always guarantees the stability of the body. It is defined on the basis of the supports that are their supporting the body. Or it also depends on the types of the forces that are acting, i.e. the three or two force system.

9. In 3D the body will be improperly constrained if the axis is intersected by the reaction forces.
a) The statement is right
b) The statement is wrong
c) The statement is right if there is ‘2D’
d) The statement is right if there is ‘support reaction’

Answer: a [Reason:] In 3D the body will be improperly constrained if the axis is intersected by the reaction forces. This is because there will be small moments which will occur in the real situations. But they will not be matched in the calculations done for determining the equilibrium. Thus the statement is right.

10. The improper constraining leading to instability occurs when ___________________
a) The reactive forces are parallel
b) The reactive forces are perpendicular
c) The reactive forces are equal
d) The reactive forces are rotational

Answer: a [Reason:] If the forces are parallel (the reactive forces) then this creates an instability. That is this is also a type of improper constraining which is resulting in instability of the structure. Thus reactive forces are parallel are resulting in the instability of the body.

11. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the sum of all the vertical forces at the supports.

a) 1280N
b) 80N
c) 200N
d) 100N

Answer: a [Reason:] As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.

12. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the vertical reaction at the support Q.

a) 707N
b) 80N
c) 200N
d) 100N

Answer: a [Reason:] As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.

13. What is partially constrained?
a) There will be less equations available for equilibrium than the reactive forces
b) There will be more equations available for equilibrium than the reactive forces
c) There will be equal equations available for equilibrium as the reactive forces
d) The support reactions are opposite to each other

Answer: b [Reason:] The situation may arise when there will be more equations available for equilibrium than the reactive forces. This condition is known as partially constrained. This is also one of the factor which is giving instability to the structure.

14. If all the reactive forces are intersecting at the common point or pass through a common axis when _____________
a) The body is in equilibrium
b) The body is said to be achieve stability but no equilibrium
c) The body is said to be improperly constrained
d) The body is in deformation

Answer: c [Reason:] If all the reactive forces are intersecting at the common point or pass through a common axis then the body is said to be improperly constrained. Whether it may be the reactive forces being parallel. Or be it the forces meeting at a common point. The body is said to be improperly constrained.

15. A homogeneous plate is shown has a mass of 100kg and is subjected to a force and a system of couple along its edge. If it is supported by a horizontal plane and a roller at R a ball and socket joint at P and a cord at Q, determine the vertical reaction at the support R.

a) 790N
b) 80N
c) 200N
d) 100N

Answer: a [Reason:] As the vertical force means that the force is going from the outer to the inner section of the plate and the horizontal force means that the force is travelling along the plane of the surface. Thus by applying the conditions for the equilibrium we get the above answer.

## Set 4

1. Just like the collinear forces for free body diagrams there are collinear couple and the net moment is taken out from it.
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:] Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

2. The simplification of the forces on the free body diagrams 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.

3. In the figure given below, calculate the value of cosγ. (γ is the angle made by the resultant vector and the z-axis)

a) 0.866
b) -0.354
c) 0.540
d) 0.354

Answer: a [Reason:] Well, the question is just a tricky one. Just subtract 60 from 90, you will get the γ, which is 30. And then apply the cosine formula for getting the components of respective axis.

4. The system of the collinear and the parallel force in free body diagrams are simplified as _________
a) The simplified collinear force system gives us a net force and the parallel force system gives us a simplified force, and then we add it vectorially
b) Such simplification is not possible
c) The simplification is usually done by not considering the directions of the both
d) The simplification is done by considering the rotations only

Answer: a [Reason:] The simplification is easy. The simplified force system gives us a net force and the parallel force system gives us a simplified force, and then we add it vectorially. Thus the vector addition at the last can be easily done and thus both can be simplified.

5. The couple is a scalar quantity and the force is vector quantity and hence only force can be simplified in free body diagrams.
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: a [Reason:] Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

6. The couple is simplified easily by the help of right hand rule in free body diagrams. But the forces simplification is not possible as there is no such system of rules so that the forces can be simplified.
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:] Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D. Forces are simplified on the basis of the algebra.

7. The couple and the other two force systems in free body diagrams can be easily simplified.
a) Statement is wrong
b) Statement is right
c) Statement is right if we remove ‘couple’ part
d) Statement is right if we remove ‘force’ part

Answer: b [Reason:] Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

8. Determine the vertical components of the reaction on the beam at pin Q.

a) 4kN
b) 3kN
c) 2kN
d) 1kN

Answer: a [Reason:] The summation of the forces needs to be zero. So does the summation of the moments need to zero. But talking about the angles, they not needed to zero. But the forces which are acting at particular angles, must needed to be equal to zero. The basic need of the forces to make the body in equilibrium.

9. The force and the couple can’t be simplified together as one is the cause and the other is the effect in free body diagrams.
a) The statement is correct and the reason given is also correct
b) The statement is wrong but the reason given is also correct
c) The statement is wrong and the reason given is also wrong
d) The statement is correct but the reason given is also wrong

Answer: c [Reason:] Both of them are vector quantities. And both of them can be easily simplified. If taken in the vector form then the task is even easier. Thus it is not necessary for the force or the couple to be vector only, even if the magnitude is taken, the simplification is done in the 2D.

10. What is a collinear system of forces for free body diagrams?
a) The force system having all the forces parallel to each other
b) The force system having all the forces perpendicular to each other
c) The force system having all the forces emerging from a single point
d) Forces cannot form a collinear system of forces, it is not possible

Answer: c [Reason:] The force system having all the forces emerging from a point is called the collinear system of force. This is a type of system of the force, which is easy in the simplification. This is because as the forces are the vector quantity, the vector math is applied and the simplification is done.

11. The main moto of the free body diagrams is to:
a) To reduce the calculation
b) To add the forces with the couples and take out the total
c) To subtract the forces with the couples and take out the total
d) To multiply the forces with the couples and take out the total

Answer: a [Reason:] The main moto of the free body diagrams is to reduce the calculation. The forces are simplified and the couples too are simplified. This gives us the total force and the total moment acting on the body. This gives us a single value of the respective thing and hence reduces the labour.

12. The couple moment and the force is divided to get the distance of the axis from the point of action of the force in free body diagrams.
a) True
b) False

Answer: a [Reason:] The couple is the cross product of the force and the perpendicular distance between the forces. And if the division of the both is done than the resulting quantity is the distance only. But care must be taken that the product is the cross product and hence sine angle must be divided too to get the distance.

13. The simplification of the couple is done for free body diagrams 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.

a) It states that the force acting on the body is a sliding vector
b) It states that the force acting on the body is a rolling vector
c) It states that the force acting on the body is a wedging vector
d) It states that the force acting on the body is a unit vector

Answer: a [Reason:] Principle of transmissibility states that the force acting on the body is a sliding vector. That is it can be applied at any point of the body. It will give the same effect as if applied at any point other that the specific point. Thus the answer.

15. Just like the collinear force system for free body diagrams there is a system of the parallel forces.
a) True
b) False

Answer: a [Reason:] There is a system so called the parallel system of the forces. This is another type of the forces. The simplification of this type of the forces is also very easy. This means that the forces in a certain direction is taken as positive and in the other direction is negative and hence the simplification is done.

## Set 5

1. Determine the magnitude of the projection of the vector force F = 100N, onto the u axis, from the figure given below.

a) 96.6N
b) 60N
c) 100N
d) 70.7N

Answer: d [Reason:] The component of the force in the u axis, it is equal to 100cos(45˚). We need to consider the triangle and then accordingly apply the trigonometry. This is one of the way of resolving the components.

2. For two vectors A and B, what is A.B (if they have angle α between them)?
a) |A||B| cosα
b) |A||B|
c) √(|A||B|) cosα
d) |A||B| sinα

Answer: a [Reason:] The dot product of the two vectors is always the product of the magnitudes of the two forces and the cosine of the angle between them. We need to consider the triangle and then accordingly apply the trigonometry. This is one of the way of resolving the components.

3. Which statement is right?
a) Communitive law: A.B =B.A
b) Multiplicative law: a(A.B) = Ax(aB)
c) Multiplicative law: A.(B+D) = (A.B) + (A.D)
d) Communitive law: a(A.B) = A.(aB)

Answer: a [Reason:] For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).

4. What is Distributive law?
a) A.B =B.A
b) a(A.B) = A.(aB)
c) A.(B+D) = (A.B) + (A.D)
d) a(A.B) = AxB

Answer: c [Reason:] For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).

5. What is multiplication law?
a) A.B =B.A
b) a(A.B) = A.(aB)
c) A.(B+D) = (A.B) + (A.D)
d) a(A.B) = AxB

Answer: b [Reason:] For three vectors A, B and D the various laws are. Communitive law: A.B =B.A. While distributive law is A.(B+D) = (A.B) + (A.D). And multiplication law is a(A.B) = A.(aB).

6. Which is true for two vector A = A1i + A2j + A3k and B = B1i + B2j + B3k?
a) A.B = A1B1 + A2B2 + A3B3
b) AxB = A1B1 + A2B2 + A3B3
c) A.B = A1B2 + A2B3 + A3B1
d) AxB = A1B2 + A2B3 + A3B1

Answer: a [Reason:] The multiplication of x, y and z components with their respective same component give a scalar, equal to 1, i.e. i.i = 1 and j.j = 1, while jxj =0. This is the basic principle of the vector algebra which needs to apply wherever needed.

7. Determine the magnitude of the force F = 300j parallel to the direction of AB?

a) 155N
b) 257.1N
c) 200N
d) 175N

Answer: b [Reason:] Force component in the direction parallel to the AB is given by unit vector 0.286i + 0.857j + 0.429k. Now (300j).(0.286i + 0.857j + 0.429k) = 257.1N. Just try to resolve the force into it’s particular components.

8. What is k.i?
a) 0
b) 1
c) -1
d) ∞

Answer: a [Reason:] As the dot product of only the same Cartesian component is unity, i.e. i.i = 1 and j.j =1, rest all remaining dot product will give 0(i.j = 0 and j.k = 0). Cross product of the same plane vectors always give zero. And dot product of the same plane vector gives a scalar quantity.

9. What is {(i.i) + (-i.j) + (-k.k) + (k.i)}.(Ai +Bj + Cz)?
a) 1
b) 0
c) A + B + C
d) -1

Answer: b [Reason:] {(i.i) + (-i.j) + (-k.k) + (k.i)} = 0. As (1 + 0 + 0 – 1). Cross product of the same plane vectors always give zero. And dot product of the same plane vector gives a scalar quantity.

10. α = cos-1(A.B/AB). What is the range of α?
a) 0˚<α<90˚
b) 0˚<α<180˚
c) 90˚<α<180C
d) 0˚<α<45˚

Answer: b [Reason:] Cosine inverse function is defined only between 0˚ to 180˚. It cannot be defined under any of the given range, because this is the principle range of the inverse cosine function.

11. What is the value of {(AxB).(C.D)x(AxB).(C.D)}? For the four vectors A, B, C and D, with A, B, C and D all lying in the same plane?
a) i + j + k
b) √3(i + j + k)
c) 0
d) -1(i + j + k)

Answer: c [Reason:] Here we are trying to do the cross product of the two vectors in the same plane. Which will give us zero. While dot product of the same plane vector will give a scalar quantity, not zero.

12. What is (AxB).(BxA); or A = A1i + A2j + A3k and B = B1i + B2j + B3k?
a) 0
b) A1B1A2B2i + A2B2A3B3j + A3B3A1B1k
c) A1B1A1B2i + A2B2A3B2j + A3B3A1B3k
d) A1B1A2B1i + A2B2A2B3j + A3B3A2B1k

Answer: a [Reason:] Here we are trying to do the cross product of the two vectors in the same plane. Which will give us zero. While dot product of the same plane vector will give a scalar quantity, not zero.

13. What is the value of θ in the figure given below ?

a) 69˚
b) 60˚
c) 55˚
d) 90˚

Answer: a [Reason:] Fab= -(3/5)j + (4/5)k ; F= (4/5)i – (3/5)j ; θ = cos-1(Fab.F) = 69˚. This is the application of the triangle over the figure. Try to resolve the components of the given force. It will be easy.

14. Refer to the diagram given below, determine the magnitude of the force F = 300j perpendicular to the direction of AB.

a) 155N
b) 257.1N
c) 200N
d) 175N