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# Multiple choice question for engineering

## Set 1

1. The theorem of Pappus and Guldinus is used to find the ____________
a) Surface area of the body
b) Surface area of the body of revolution
c) Surface area of the body of linear motion
d) Surface area of the body of rectangular motion

Answer: b [Reason:] The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve being rotated can be made to be calculated from this theorem.

2. The theorem of Pappus and Guldinus states that the area of the revolving curve is ______________
a) Product of the area, length of generated curve and the radius vector
b) Product of the area, length of generated curve and the perpendicular distance from axis
c) Product of the volume, length of generated curve and the radius vector
d) Product of the volume, length of generated curve and the perpendicular distance from axis

Answer: b [Reason:] The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve. It is just the product of the area, length of generated curve and the perpendicular distance from axis.

3. The theorem of Pappus and Guldinus is used to find the ____________
a) Surface area of the body
b) Volume of the body of revolution
c) Surface area of the body of linear motion
d) Surface area of the body of rectangular motion

Answer: b [Reason:] The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve being rotated can be made to be calculated from this theorem.

4. Determine the surface area of the structure when rotated about the ray P.

a) 134m2
a) 143m2
a) 154m2
a) 169m2

Answer: a [Reason:] The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve. It is just the product of the area, length of generated curve and the perpendicular distance from axis.

5. Product of the area, ______________________ and the perpendicular distance from axis are being used in the theorem to find the area of the revolution.
a) Length of generated curve
c) Length of generated length vector
d) Length of generated area vector

Answer: a [Reason:] The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve. It is just the product of the area, length of generated curve and the perpendicular distance from axis.

6. The distance used in the theorem is the distance travelled by ______________
a) Body
b) Body’s centroid
c) Body’s length vector

Answer: b [Reason:] The theorem is used to find the surface area and the volume of the revolving body. Thus the surface area and the volume of any 2D curve. It is just the product of the area, length of generated curve and the perpendicular distance from axis. The distance being the distance travelled by the centroid.

7. Product of the Volume, ______________________ and the perpendicular distance from axis are being used in the theorem to find the volume of the revolution.
a) Area of generated curve
c) Area of generated length vector
d) Area of generated area vector

Answer: a [Reason:] The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve. It is just the product of the volume, area of generated curve and the perpendicular distance from axis.

8. The maximum value of the frictional force that can be applied to the composite body under which the theorem of the Pappus and Guldinus is going to be applied is called _________
a) Limiting Friction
b) Non-Limiting Friction
c) Limiting Action Friction
d) Non-Limiting Action Friction

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. Thus the maximum values is called as limiting friction.

9. Determine the volume of the structure when rotated about the ray P.

a) 47.6m3
a) 43m3
a) 14m3
a) 19m3

Answer: a [Reason:] The theorem is used to find the surface area and the volume of the revolving body. This is done by using simple integration. Thus the surface area and the volume of any 2D curve. It is just the product of the area, length of generated curve and the perpendicular distance from axis.

10. When the body which is applied forces come in the stage of the limiting friction then the body over which this theorem is to be applied is termed as to come in ___________ equilibrium.
a) Unstable
b) Stable
c) Non-stable
d) Improper Stable

Answer: a [Reason:] As the limiting friction is the maximum value of the frictional forces. Thus if more force is applied to the body then the body is going to move forward. Because the two surfaces are in contact and the friction applies at that surface only, resisting the motion of the surface. Thus the name unstable equilibrium.

11. We use sometimes the measures to know the direction of moment. It is done by right handed coordinate system. Which is right about it for the bodies over which this theorem is going to be applied (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.

12. What is not the condition for the equilibrium in three dimensional system of axis for the bodies for which this theorem is going to be applied?
a) ∑Fx=0
b) ∑Fy=0
c) ∑Fz=0
d) ∑F≠0

Answer: d [Reason:] For the equilibrium in the three dimensional system of axis we have all the conditions true as, ∑Fx=0, ∑Fy=0 and ∑Fz=0. Also we have the summation of the forces equal to zero. Which is not a non-zero value.

13. What is a collinear system of forces for the bodies over which this theorem is to apply?
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.

14. The system of the collinear and the parallel force for the bodies over which this theorem is to be applied 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.

15. If solving the question in 3D calculations is difficult, then use the 2D system to make the use of the theorem.
a) True
b) False

Answer: a [Reason:] The answer is obviously yes. If we are having any difficulty in making the vector components, then we can go in 2D. As if the particle is in equilibrium, the net force will be zero. No matter where you see first. Net force is zero.

## Set 2

1. What is not the condition for the equilibrium in three dimensional system of axis?
a) ∑Fx=0
b) ∑Fy=0
c) ∑Fz=0
d) ∑F≠0

Answer: d [Reason:] For the equilibrium in the three dimensional system of axis we have all the conditions true as, ∑Fx=0, ∑Fy=0 and ∑Fz=0. Also we have the summation of the forces equal to zero. Which is not a non-zero value.

2. State true or false. We first make equilibrium equations and then the free body diagram and then solve the question?
a) True
b) False

Answer: b [Reason:] We first make the free body diagram and then we make the equilibrium equations to satisfy the given conditions. This helps us to solve the question easily. As this reduces the part of imagination and increases accuracy too.

3. In the diagram given below, coordinates of D is (1, -2, 2), C (-2, 0, 0) and B are as shown. The dark region is the cables holding the weight of 600N at origin. Find the tension in the AD section.

a) 900N
b) 693N
c) 646N
d) 0N

Answer: a [Reason:] As the system is in equilibrium so we need to balance the forces. So when apply the condition of net force to be zero in the z direction, we get (2/3)FAD = 600N. This gives us force along AD be 900N.

4. In the diagram given below, coordinates of D is (1, -2, 2), C (-2, 0, 0) and B are as shown. The dark region is the cables holding the weight of 600N at origin. Find the tension in the AB section.

a) 900N
b) 693N
c) 646N
d) 0N

Answer: b [Reason:] As the system is in equilibrium so we need to balance the forces. So when apply the condition of net force to be zero in the y direction, we get FAB cos30 = (2/3)*900. This gives us force along AB be 693N.

5. 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.

6. Determine the value of the q, parallel to the z axis. That is the point of intersection of the projections of the points A, B and C parallel to the xy plane. With the distance between the tri-section point and the points A, B and C be equal to 0.6m.

a) 51.9cm
b) 51.9mm
c) 51.9m
d) 5.19mm

Answer: a [Reason:] The application of the equilibrium equation will yield the result. That is the resultant along the z-axis will remain zero. Which give the value of γ as 50˚. And therefore q=51.9cm.

7. ∑Fx=0, ∑Fy=0 and ∑Fz=0 are vector equations.
a) True
b) False

Answer: b [Reason:] The answer is false as the equations asked are scalars. As we make the net sum of the forces along the axis equal to zero. Of course this equation comes from the solving the vector forms, but still the result is a scalar, hence the equations are scalar.

8. When the body is in equilibrium then which of the following is true?
a) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude
b) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude square
c) We equate all the components of the forces acting on the body equal to their resultant vector’s magnitude square root
d) We equate all the components of the forces acting on the body equal to zero

Answer: d [Reason:] Yes, we equate all the components of the three axis equal to zero. That is the resultant of the forces along the three axis are being equated to zero. This brings in that there is no net force along any direction. Hence equilibrium.

9. If solving the question in 3D calculations is difficult, then use the 2D system and then equate the total net force to zero.
a) True
b) False

Answer: a [Reason:] The answer is obviously yes. If we are having any difficulty in making the vector components, then we can go in 2D. As if the particle is in equilibrium, the net force will be zero. No matter where you see first. Net force is zero.

10. If the resolved force or the force which you get as the answer after solving the question is negative, then what does this implies?
a) The force is in the reverse direction w.r.t the direction set in the free body diagram
b) The force is not in the reverse direction w.r.t the direction set in the free body diagram
c) The force component is not possible
d) The force is possible, but in the direction perpendicular to the resultant force

Answer: a [Reason:] The negative sign implies things in the opposite manner. If the force is coming negative this doesn’t means that it is impossible. But it means that the force is in the opposite direction w.r.t the direction set by you in the free body diagram.

11. An electromagnet crane is carrying the electromagnet with the help of the three cables. But the electromagnet is not stable because of the wind. What is science behind the cause?
a) The wind is making the net force of the body equal to a non-zero value
b) The wind is making the net force of the body equal to zero value
c) The wind is making the net force of the body equal to a non-zero value but is supporting the equilibrium
d) The wind is making the net force of the body equal to zero value and supporting equilibrium

Answer: a [Reason:] Any body is in equilibrium only if the net force along the three axis is zero. But in this case the wind is not helping the body to do so. The science behind this is that the resultant forces are being equated to a non-zero value by the wind. Hence unstable.

12. If any body is tied to three or more ropes, and then is allowed to achieve its equilibrium. Then the equilibrium achieved is achieved w.r.t what?
a) The three axis of the body
b) The ground
c) The ropes direction
d) The weight direction

Answer: b [Reason:] Yes, the equilibrium is being achieved w.r.t the ground. Like the motion w.r.t ground need be zero. That is the relative velocity of the object or the body must be zero w.r.t the ground. This means motion is in equilibrium.

## Set 3

1. 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

Answer: d [Reason:] 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.

2. 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.

3. Which of the following is correct?
a) The two force members doesn’t apply the moments to the body
b) The three force members doesn’t apply the moments to the body
c) Only the two force members apply the moments to the body
d) Both the three and two force members apply the moments to the body

Answer: d [Reason:] The force members doesn’t defines whether the moment will be applied or not. They are basically the forces only. Thus if there is a force applied on the body, there will be a moment produced by them. If not then probably the forces might be collinear.

4. The three member forces are greatly influencing the moment than the two force members.
a) True
b) False

Answer: b [Reason:] The influence of the moment on the body is determined by the number of the forces acting on the body. It depend on the magnitude of the force. It also depend whether the forces are collinear or not. Thus the number of forces are not the only parameter for the determination of the moment.

5. The three member forces apply three different moments and the two members apply two different moments on the body.
a) True
b) False

Answer: b [Reason:] Never judge the application of the moment of the force applied on the body by the number of the forces being acted on the body. What is two of the forces becomes collinear and are having a zero distance from the axis of rotation. Thus the three and two force member apply moments according to the situation, whether the distance is zero or not.

6. For two force members to be in equilibrium when _____________
a) They both must not be collinear
b) They must be of different magnitude
c) They must be in the same direction
d) They must be in the opposite direction cancelling each other

Answer: d [Reason:] Simply, for the equilibrium the net force must be zero. That is the forces must be collinear if equilibrium is to be established. And they must be in the opposite directions. They also must be of same magnitude, cancelling each other.

7. Determine the force in the section RS.

a) 11.3N
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.

8. Moment equilibrium for the three force members will only be satisfied if_____________
a) Three forces are in different dimensions
b) The forces are in the same direction
c) The forces are concurrent
d) The forces are perpendicular

Answer: c [Reason:] The moment equilibrium for the three force members is satisfies only when the three forces are concurrent. That is the forces form a parallel system. That is the net force on the three axis turns out to be zero. This will only happen if the forces are in the same plane.

9. Which of the following statement for the three force system is true?
a) The moment need not to be seen for the equilibrium, they are always in equilibrium
b) The forces are not always in the equilibrium
c) The forces are always in equilibrium
d) The moments are always in equilibrium

Answer: b [Reason:] The forces in the three force system is not always in the equilibrium. The equilibrium is established when the forces cancels out each other. Also when the net moment is zero. Then only the equilibrium is established in the three force system.

10. Determine the horizontal components of the reaction on the beam at pin Q.

a) 8kN
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.

11. 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.

12. All the forces need to be collinear in the three force system. Then only they will for the equilibrium state.
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: d [Reason:] The forces need to be collinear. If they are not so then the equilibrium is not possible. If they are parallel too, then it is assumed that they are meeting in the infinity. And hence the equilibrium is established between the forces. Thus the forces must be collinear.

13. 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.

14. 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.

15. The three force system can also be in the equilibrium if_________
a) All the forces are parallel to each other heading towards the same direction
b) The force components cancel each other
c) The forces are very small in magnitude
d) The forces are very huge in magnitude

Answer: b [Reason:] Even if the forces components cancels each other than the body is said to be in equilibrium. Also it should satisfy whether the moments caused by the forces are equal to zero or not. This means if the moment caused and the net force is zero the body is in equilibrium.

## Set 4

1. A ____________ is a simple machine that is used as to transfer applied forces into much larger forces.
a) Wedge
b) Beam
c) Pillar
d) Bridges

Answer: a [Reason:] The main thing about the wedges is that the wedge is a simple machine that is used as to transfer applied forces into much larger forces. This means that the wedges are the means of force transfer. This machine is very useful in the industries, and it has a wide application.

2. Wedges are used to transfer heavy loads.
a) True
b) False

Answer: a [Reason:] The main thing about the wedges is that the wedge is a simple machine that is used as to transfer applied forces into much larger forces. This means that the wedges are the means of force transfer. This machine is very useful in the industries, and it has a wide application.

3. The blocks of heavy weights are being able to lift from the help of the wedges.
a) True
b) False

Answer: a [Reason:] The main thing about the wedges is that the wedge is a simple machine that is used as to transfer applied forces into much larger forces. This means that the wedges are the means of force transfer. This machine is very useful in the industries, and it has a wide application.

4. The normal force exerted by the surface of the wedge is normal to the surface of the ________
a) Base of the wedge
b) Base of the body residing over it
c) Base of the body just neighbour to the wedge
d) Earth’s surface

Answer: b [Reason:] As we know the normal forces act perpendicular to the surfaces of the body kept over the wedges. Thus the normal force exerted by the surface of the wedge is normal to the surface of the base of the body kept over the wedge. The wedges are very useful in the industries, and it has a wide application.

5. Which one is not the condition for the equilibrium in free body diagram for calculation of the normal forces along the body kept over the wedge, consider all forces to be straight and linear?
a) ∑Fx=0
b) ∑Fy=0
c) ∑Fz=0
d) ∑F≠0

Answer: d [Reason:] For the equilibrium in the three dimensional system of axis we have all the conditions true as, ∑Fx=0, ∑Fy=0 and ∑Fz=0. Also we have the summation of the forces equal to zero. Which is not a non-zero value.

6. The coefficient of friction between the body being slided over the wedge and the wedge surface is generally determined by ____________
a) Written over the Body
b) Experiments
c) Weighing the body
d) Measuring length of the body

Answer: b [Reason:] The coefficient of the friction is generally determined by the help of experiments. Many experiments are done on the body. Try and error methods are involved. And the final observations are being taken out. Then average of all the final answers resulted in the experiments is done.

7. When does the two wedge system is termed as self-locking system?
a) If friction forces hold the block in plane
b) If friction forces doesn’t hold the block in plane
c) If friction forces hold the block in phase
d) If friction forces doesn’t hold the block in phase

Answer: a [Reason:] If friction forces hold the block in plane the two wedge system is termed as self-locking system. This is generally the concept used to lift up the boxes and then it is also used as to make the very heavy works easy. Thus the wedges are very useful in the industries, and it has a wide application.

8. Determine the normal force at B in the wedge shown. Take the value of coefficient of friction to be 0.3. Assume that the block doesn’t slip at C.

a) 2452 N
b) 215 KN
c) 3150 N
d) 415 KN

Answer: a [Reason:] The normal force at A is 2381 N. The normal force at B is 2452.5 N. The angle of the wedge over which the block is being slided is generally taken out by the help of the tangent inverse trigonometric function. Thus the answer.

9. In the free body diagrams involving the wedges we have use of vector math, so 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.

10. What is j.j?
a) 0
b) 1
c) -1
d) ∞

Answer: b [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.

11. 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. This is the concept used in the solving of the problems related to wedges.

12. Sometimes in the calculations involving the wedges, there are situations when there is a toppling effect on the body. In that if 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.

13. The angle of the inclination of wedge over which the block is sliding is determined by which of the following trigonometric function?
a) Tangent Inverse
b) Cosine
c) Sine
d) Secant

Answer: a [Reason:] The angle of the wedge over which the block is being slided is generally taken out by the help of the tangent inverse trigonometric function. It is the ratio of the frictional force to the normal force. This ratio is kept inside the inverse function.

14. In the simplification of the forces applied in the wedges net force acts at the ___________ of the loading body.
a) Centroid
b) The centre axis
c) The corner
d) The base

15. Determine the minimum amount of the force P required to remove the wedge shown. Take the value of coefficient of friction to be 0.3. Assume that the block doesn’t slip at C.

a) 1.15 KN
b) 2.15 KN
c) 3.15 KN
d) 4.15 KN

Answer: a [Reason:] The normal force at A is 2381 N. The normal force at B is 2452.5 N. The angle of the wedge over which the block is being slided is generally taken out by the help of the tangent inverse trigonometric function. Thus the answer.

## Set 5

1. The principle of work was proposed by________________
a) Mathematician Jean Bernoulli
b) Physios Jean Bernoulli
c) Chemist Jean Bernoulli
d) John Jean Bernoulli

Answer: a [Reason:] The concept of work was proposed by Jean Bernoulli. He was a mathematician. It was proposed in 18th century. It gave us various alternative methods to calculate the work done. Thus the answer.

2. Determine the horizontal force acting in the given figure.

a) 80cos30
b) 60cos30
c) 40cos30
d) 8cos30

Answer: a [Reason:] The net forces acting on the body is shown by the help of the resultant forces. There are two types, first the frictional and the second is the normal. This is because the resultant forces have the sum of all the forces which are acting on the direction which is same.

3. Which of the following is correct?
a) Work done is of one type only
b) Work done is of two type only
c) Work done is of three type only
d) Work done is of infinite type

Answer: d [Reason:] The work done is of many types. They are countless. For example the work can be done by moving, pushing or pulling. Or can be done by car, bus, truck or any other vehicle. Thus work can be done in many ways.

4. We first make equilibrium equations of the body by considering all the three dimensional forces and then the free body diagram is made and solved.
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: d [Reason:] We first make the free body diagram and then we make the equilibrium equations to satisfy the given conditions. This helps us to solve the question easily. As this reduces the part of imagination and increases accuracy too.

5. If solving the question in 3D calculations is difficult, then use the 2D system and then equate the total net force to zero, thus the method for solving the work done.
a) True
b) False

Answer: a [Reason:] The answer is obviously yes. If we are having any difficulty in making the vector components, then we can go in 2D. As if the particle is in equilibrium, the net force will be zero. No matter where you see first. Net force is zero.

6. If the body is in equilibrium, but it having a rotational curled ray shown in the free body diagram then:
a) The diagram is wrong
b) Such rotations can’t be shown in the fbds(free body diagrams)
c) The ray shown may be correct, but the body is not said to be in equilibrium
d) The body is said to be in equilibrium only, as the other forces will cancel out that rotation and the net work done will be zero

Answer: d [Reason:] The body having equilibrium will not rotate at any cost. Yes, the diagram may contain the rotational array showing the couple being acted over the structure. But the thing is that the forces, i.e. the other forces which are outside the dependency of this rotation will cancel out this rotation and thus the body is in equilibrium.

7. If the resolved force or the force which you get as the answer after solving the question is negative, then what does this implies?
a) The force is in the reverse direction w.r.t the direction set in the free body diagram
b) The force is not in the reverse direction w.r.t the direction set in the free body diagram
c) The force component is not possible
d) The force is possible, but in the direction perpendicular to the resultant force

Answer: a [Reason:] The negative sign implies things in the opposite manner. If the force is coming negative this doesn’t means that it is impossible. But it means that the force is in the opposite direction w.r.t the direction set by you in the free body diagram.

8. Determine the vertical force acting in the given figure.

a) 236N
b) 600n
c) 403N
d) 830N

Answer: a [Reason:] The net forces acting on the body is shown by the help of the resultant forces. There are two types, first the frictional and the second is the normal. This is because the resultant forces have the sum of all the forces which are acting on the direction which is same.

9. What does the Newton’s third law states for the work done?
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.

10. The net moment of the body is zero that means the work done by 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: b [Reason:] The net moment of the body is zero that doesn’t means that the work done by the force and the rotational axis is zero. Work done is something different. It does not depend on the rotational axis. It only depends on the distance. And the forces.

11. ∑Fx=0, ∑Fy=0 and ∑Fz=0 are vector equations for the three dimensions. They are satisfied when the body is achieved it state of equilibrium, and then the work done is calculated.
a) True
b) False

Answer: b [Reason:] The answer is false as the equations asked are scalars. As we make the net sum of the forces along the axis equal to zero. Of course this equation comes from the solving the vector forms, but still the result is a scalar, hence the equations are scalar.

12. Which of the following needs to zero for the perfect equilibrium for the calculation of the work?
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.

13. What is Newton’s second law for work?
a) The rate of change of momentum is equal to the force applied
b) The rate of change of distance is equal to the force applied
c) The rate of change of momentum is equal to the moment applied
d) The rate of change of momentum is equal to the work applied

Answer: a [Reason:] The rate of change of momentum is equal to the force applied to the body. This is the second law which is used to calculate the work done in the body by the forces. This has a very vast application on the industrial sector and engineering sector.

14. The supports in the 3D are having more than three reaction forces. Because they are having three axis on which the components of the work done need to be 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: d [Reason:] As 3D is defined as the three axis system, we have to consider the equilibrium in all the three axis. This will make the equilibrium go on all the axis of the 3D space. And hence will cancel all the forces.

15. If five forces are acting on the single particle and having an angle of 72˚ between each and are collinear, then_____________
a) The net force acting on the body is zero and the net work done is also zero
b) The net force acting on the body is horizontal
c) The net force acting on the body is vertical but net work done is non-zero
d) The net force acting on the body is at an angle of 45