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# Multiple choice question for engineering

## Set 1

1. In the support system of the bridges and trolley wheel ____________ form the main loading carrying element in the structure.
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.

2. What is the dot product of the components of the force vector shown in the figure, i.e. the dot product of the z-axis component and the y-axis component of the force?

a) 0
b) 200cos60°
c) 200sin45°
d) 200cos30°

Answer: a [Reason:] The dot product of any two vectors is having the cosine function in it. It is being multiplied by product of the magnitudes of the vectors. So if the angle is 90°, then the value of cosine function would be zero, thus 0. And the value of the sine angle is 1, thus the result.

3. The assumptions for the calculations for cables under distributed load 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.

4. The force on the cables under distributed load 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.

5. The assumptions for the calculations are done for the cables under distributed load. 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.

6. The various points in the cables under distributed load 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.

7. Due to which property the cables under distributed load, 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.

8. Flexible cables under distributed load 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.

9. The tensile force acting on the cables under distributed load 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. If the unknown variables in the calculations for cables under distributed load 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.

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.

12. The cables under distributed load 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.

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.

14. What is the magnitude of the resultant vector’s unit vector? (Resultant vector of the two vectors shown in the figure below)

a) 1N
b) 225N
c) 110N
d) 55N

Answer: a [Reason:] The question asked is asking for the magnitude of the unit vector of the resultant vector, thus the answer is 1. Whether the magnitude of the vector be any quantity, but the unit vector will have the magnitude equal to unity. And the direction given by the unit vector will be in the same direction as that of the vector.

15. Being inextensible the cables under distributed load 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.

## Set 2

1. Which of the following statement is true?
a) A scalar is any physical quantity that can be completely specified by its magnitude
b) A vector is any positive or negative physical quantity that can be completely specified by its magnitude
c) A scalar is any physical quantity that requires both a magnitude and a direction for its complete description
d) A scalar is any physical quantity that can be completely specified by its direction

Answer: a [Reason:] A scalar is any positive or negative physical quantity that can be completely specified by its magnitude. Examples of scalar quantities include length, mass, time, etc.

2. For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents:
a) Their magnitude’s square and direction of the line of action respectively
b) Their magnitude and direction of the line of action respectively
c) Magnitude’s square root and direction of the line of action respectively
d) Magnitude’s square and ratio of their lengths respectively

Answer: b [Reason:] For two vectors defined by an arrow with a head and a tail. The length of each vector and the angle between them represents their magnitude and direction of the line of action respectively. The head/tip of the arrow indicates the sense of direction of the vector.

3. If a vector is multiplied by a scalar:
a) Then its magnitude is increased by the square root of that scalar’s magnitude
b) Then its magnitude is increased by the square of that scalar’s magnitude
c) Then its magnitude is increased by amount of that scalar’s magnitude
d) You cannot multiply the vector with a scalar

Answer: c [Reason:] If a vector is multiplied by a scalar then its magnitude is increased by amount of that scalar’s magnitude. When multiplied by a negative scalar it going to change the directional sense of the vector.

4. All the vectors quantities obey:
b) Parallelogram law of multiplication
c) Parallelogram law of addition of square root of their magnitudes
d) Parallelogram law of addition of square of their magnitudes

Answer: a [Reason:] All the vectors quantities obey parallelogram law of addition. Two vectors A and B (can be called as component vectors) are added to form a resultant vector. R = A+B.

5. A force vector with magnitude R and making an angle α with the x-axis is having its component along x-axis and y-axis as:
a) Rcosine (α) and Rsine(α)
b) Rcosine (180-α) and Rsine(α)
c) Rcosine (180-α) and Rsine(180+α)
d) Rcosine (α) and Rsine(180+α)

Answer: a [Reason:] The component along x-axis is the cosine component of the vector. And the y-axis component of the vector is sine component, if the angle is being made with the x-axis. And 180- α for some of the trigonometric function may change their sign.

6. Dividing the X-axis component and the Y-axis component of the of the vector making an angle with Y-axis α will give us.
a) Cot α
b) Tan α
c) Sec α
d) 1

Answer: b [Reason:] As the X-axis component of the vector becomes cos(90- α) and the Y-axis component becomes sin(90- α).Thus the division of both will give us Tan α.

7. Vector shown in the figure below have a length of 3m and the angles shown A and B are 60 and 30 degrees each. Calculate the X-axis and Y-axis components:

a) 2.59m and 1.50m respectively
b) 1.50m and 2.59m respectively
c) 3cos60 and 3sin30 respectively
d) 3sin60 and 3sin30 respectively

Answer: a [Reason:] The sine and the cosine components of the given vectors considering the angle B as the only angle of consideration comes 1.5m and 2.59m.

8. Shown as in the figure below, A=60 degree and B=30 degree. Calculate the total length obtained by adding the x-axis component of both the vectors.

a) 3.23m
b) 4.35m
c) 2.50m
d) 1.5m

Answer: a [Reason:] After getting the cosine components of the given vectors we obtain the total length of the x-axis components to be 3cos60 + 2cos30 = 3.23.

9. The magnitude of the resultant of the two vectors is always_____________
a) Greater than one of the vector’s magnitude
b) Smaller than one of the vector’s magnitude
c) Depends on the angle between them
d) Axis we choose to calculate the magnitude

Answer: c [Reason:] Yes, the magnitude of the resultant of the two vectors always depends on the angle between them. It might be greater or smaller than one of the vector’s length. For perfectly saying, it does depends upon the angle between them.

10. If two equal vector forces are mutually perpendicular then the resultant force is acting at which angle as compared to one of the vector?
a) 45 degree
b) 90 degree
c) 180 degree
d) 0 degree

Answer: a [Reason:]s: The vectors are mutually perpendicular, this means that the angle between the forces is 90 degree. Thus the resultant will form at 45 degrees to any of the vector.

11. What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?
a) It is either in the 1st quadrant or in 2nd quadrant
b) It is either in the 1st quadrant or in 3rd quadrant
c) It is either in the 1st quadrant or in 4nd quadrant
d) Only in the 1st quadrant

Answer: c [Reason:] If one is heading towards positive X-axis and the other is in the other direction opposite to the first one, with both having same length and having an angle between them being obtuse, means that the direction is to be in the direction of either 1st quadrant or in 4nd quadrant.

12. Force vector R is having a______________
a) Length of R and a specific direction
b) Length of R
c) A specific direction
d) Length of magnitude equal to square root of R and a specific direction

Answer: a [Reason:] As it is a force vector, it means it is going to have a direction and a magnitude. The magnitude is not the square root of R, R is just the magnitude of the vector given.

13. The resultant of three equal vectors having mutual angles being 120 degree and being originated from a single point is zero.
a) True
b) False

Answer: a [Reason:] As one can imagine three vectors coming out of a single point and are having a 120 degree angle with their adjacent ones, the resultant would be zero.

14. Every point on the force vector is having the same magnitude and the same direction as the whole force vector have.
a) True
b) False

Answer: b [Reason:]s: The vector is made by joining the final and the starting point. If we consider any arbitrary point then the length would be calculated w.r.t the starting point, which might give different magnitude but same direction.

## Set 3

1. Determine the resultant moment caused by the forces in vector

a) 30i + 40j – 60k Nm
b) 30i – 40j – 60k Nm
c) 30i + 40j + 60k Nm
d) 30i – 40j + 60k Nm

Answer: d [Reason:] As we know that the moment is the cross product of the force and the distance between the point of contact of the force and the point about which moment needs to be calculated. Here distance r1 =5j m and r2 = 4i + 5j – 2k m. Thus doing the cross product will give the answer.

2. Which of the following is correct 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.

3. What does FLsinθ means/represents 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.

4. The basic way of getting the direction of the moment caused by the force 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.

5. If any force is applied in the direction of the positive x-axis, and there are three different point 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. 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______________
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.

7. : 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?
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.

8. We can express the force in the Cartesian form.
a) True
b) False

Answer: a [Reason:] Yes, we can prepare the moment in the Cartesian form. As the moment in the 3D is the vector. Which can be easily made in the form of Cartesian coordinates. Also it can be seen that the moment is the cross product of the force and the distance, hence the moment is in vector form.

9. M = ∑(rxF) represents what?
a) The total distance of the point of contact of the and the axis of rotation
b) The total moment of the forces
c) The total force acting on the body
d) The equation is wrong, it must be Fxr

Answer: b [Reason:] The given equation represents the total moment of the forces which are acting on the body. That is the summation of all the rxF. Where the r is the distance of the axis from the point of action of the force on the body. And thus this is the total summation of the moments of all the forces acting on the body.

10. If a 12m high tree is being pulled by the tractor, by a rope tied over the top. With the tractor at a linear distance of 12m and 4m away perpendicularly from the tree. If the force applied by the tractor is 2KN then what is the moment caused about the roots of the tree?
a) -16.5i+7.51j KNm
b) -16.5i+5.51j KNm
c) -16.5i+5.51j KNmm
d) -16.5i+7.51j KNm

Answer: b Answer: The force developed is 2KN, and the roots are having the coordinate (0, 0, 0). Coordinates of the top of the tree is (0, 0, 12). The tractor’s coordinates are (4, 12, 0). Thus applying the cross product on the force and the distance of the tractor from the roots we get the answer as -16.5i+5.51j KNm.

11. If F = F1+F2, then moment of this force F about a point at a distance r is M=rxF1 + rxF2.
a) True
b) False

Answer: a [Reason:] If F = F1+F2, then moment of this force F about a point at a distance r is M=rxF1 + rxF2. As M = rx(F) = rx(F1 + F2) = rxF1 + rxF2. This is known as the principle of moments. As the force is a vector quantity thus this is the distributive property which we apply to get the answer.

12. Determine the moment of the force about the point X.

a) 11.2 Nm
b) 10 Nm
c) 7Nm
d) 8Nm

Answer: a [Reason:] As we know that the moment is the cross product of the force and the distance between the point of contact of the force and the point about which moment needs to be calculated. Thus forming the distance vector and then crossing it with the force will give us the answer. Remember force also needs to be in the vector form for doing the cross product.

13. Determine the moment about the point Q by the force shown as 400N.

a) -98.6kN
b) 98.6kN
c) -98.6iN
d) -98.6jN

Answer: a [Reason:] As we know that the moment is the cross product of the force and the distance between the point of contact of the force and the point about which moment needs to be calculated. Thus forming the distance vector and then crossing it with the force will give us the answer. Remember force also needs to be in the vector form for doing the cross product.

14. Determine the moment about the point P.

a) 460Nm
b) 500Nm
c) 705Nm
d) 0Nm

Answer: a [Reason:] As we know that the moment is the cross product of the force and the distance between the point of contact of the force and the point about which moment needs to be calculated. Thus forming the distance vector and then crossing it with the force will give us the answer. Remember force also needs to be in the vector form for doing the cross product.

15. Determine the magnitude of the resultant moment caused by the forces.

a) 78.1Nm
b) 25Nm
c) 110Nm
d) 80Nm

Answer: a [Reason:] As we know that the moment is the cross product of the force and the distance between the point of contact of the force and the point about which moment needs to be calculated. Here distance r1 =5j m and r2 = 4i + 5j – 2k m. Thus doing the cross product will give the answer.

## Set 4

1. What is the dot product of two vectors which are having magnitude equal to unity and are making an angle of 45°?
a) 0.707
b) -0.707
c) 1.414
d) -1.414

Answer: a [Reason:] The dot product of two vectors having the angle between them equal to 45° will have the product of the vector’s magnitude. As the vectors are of unit magnitude, their product will be unity. Thus the magnitude factor would be cosine function at 45 °.

2. Mathematically, for two vectors A and B of any magnitude, the cross product of both, i.e. AxB = given by:
a) |A||B|sinØ
b) |A||B|
c) |A||B|cosØ
d) |A||B|sin(180°+Ø)

Answer: a [Reason:] The cross product of two vectors gives a vector which is perpendicular to both of the vectors. And the mathematic equation for the same is given by: |A||B|sinØ. And the dot product of the same by any of the other two vectors will give the answer zero, as perpendicular.

3. Commutative law is valid for the cross product of two vectors. (Commutative law: PxQ = QxP; for two vectors P and Q)
a) True
b) False

Answer: b [Reason:] This statement is wrong. It is not possible, unless we apply a negative sign to the RHS of the equation. That is PxQ = -(QxP). It is because, if you curl your wrist from one vector towards another vector, the thumb projected will give the direction of the cross product. Thus if you reverse the direction, negative sign is necessary.

4. Which among the following is the distributive law for the cross product of three vectors?
a) Px(Q+S) = (PxQ) + (PxS)
b) Px(QxS) = (PxQ) + (PxS)
c) Px(QxS) = (PxQ) x (PxS)
d) Px(Q+S) = (PxQ) + (QxS)

Answer: a [Reason:] The distributive law works just like the simple multiplication of the constant before the brackets. That is in the equation Px(Q+S) = (PxQ) + (PxS), P is crossed by Q and S both. This is simple as, if we first add the two vectors and then do the cross product or we first do the cross product and the do the sum.

5. Which statement is true? (For three vectors P, Q and R)
a) Associative law for cross product: (PxQ)xS = Px(QxS)
b) Associative law for cross product: (PxQ)xS ≠ Px(QxS)
c) Associative law for cross product: (PxQ)xS > Px(QxS)
d) Associative law for cross product: (PxQ)xS < Px(QxS)

Answer: b [Reason:] The associative law is defined in the cross product of three vectors. This property is though valid for the dot product. But for the cross product, it is not true. It is because, in the dot product the final result is the scalar quantity, but in cross product it is the direction too. Thus the answer.

6. Which of the following is true?
a) i x i =1
b) j x i = -j
c) k x j = -i
d) k x k = 1

Answer: c [Reason:] As the mathematic equation for the cross product is having a cosine function in it, in which the angle used in the function is the angle between the vectors. Thus the cross product will be zero if the angle between them is 90.

7. Which of them is not correct?
a) j x j = 0
b) j x k = i
c) j x i = k
d) j x i = -k

Answer: c [Reason:] As asked, the one which is not correct is the third one. The product is containing the cosine function, and the angle which is going to be inserted in the function is the angle between the vectors. Thus if the angle is 90, then the cross will be zero.

8) 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.

9) The tendency of a force to rotate the body is called the moment of the force.
a) True
b) False

Answer: a [Reason:] The moment of the force about a axis or a point gives the measure of the tendency of the force. It is the cause of the body’s rotation, about that point or at that axis. Thus, the tendency of a force to rotate the body is called the moment of the force.

10) 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.

11) What is Varigon’s Theorem? (M = Moment, F= Force vector, R= Radius vector)
a) M = R x F (F = F1 + F2 + F3 + … vectorially adding all the forces)
b) |A||B|sinØ
c) AxB)xS ≠ Px(QxS)
d) Px(Q+S) = (PxQ) + (PxS)

Answer: a [Reason:] For many vectors acting on the body, Varigon’s Theorem is defined as M = R x F (F = F1 + F2 + F3 + … vectorially adding all the forces). This is just the giving the cross product of individual force and radius vectors and thus the sum is the total moment produced.

12. What is the mixed triple product of three vectors?
a) S.(PxQ)
d) Sx(PxQ)
c) S.(P.Q)
d) Sx(P.Q)

Answer: a [Reason:] It is the scalar expression. It is the dot product of the vector to the vector, which is the result of the cross vector product of two vectors. And if two vectors are held together in the equation by a dot “.”, then the answer which you get is the scalar quantity.

13. What is the angle made by the vector shown in the figure, with the z-axis?

a) 45°
b) 60°
c) 30°
d) 90°

Answer: c [Reason:] The question is the tricky one, just the imagination of the viewer is to be enhanced. But is one needs to go with the calculation, one can go and the answer would be 30°. Or simply it is 90° – 60° = 30°.

14. What is the dot product of the components of the force vector shown in the figure, i.e. the dot product of the z-axis component and the y-axis component of the force?

a) 0
b) 200cos60°
c) 200sin45°
d) 200cos30°

Answer: a [Reason:] The dot product of any two vectors is having the cosine function in it. It is being multiplied by product of the magnitudes of the vectors. So if the angle is 90°, then the value of cosine function would be zero, thus 0. And the value of the sine angle is 1, thus the result.

15. What is the magnitude of the resultant vector’s unit vector? (Resultant vector of the two vectors shown in the figure below)

a) 1N
b) 225N
c) 110N
d) 55N

Answer: a [Reason:] The question asked is asking for the magnitude of the unit vector of the resultant vector, thus the answer is 1. Whether the magnitude of the vector be any quantity, but the unit vector will have the magnitude equal to unity. And the direction given by the unit vector will be in the same direction as that of the vector.

## Set 5

1. The ____________ forces are used are used in the method of sections for the calculation of the internal forces.
a) Internal rotational
b) Couple rotational
c) Translational
d) External

Answer: d [Reason:] The calculations of the method of sections involve the making of the free diagrams and then use external forces to determine the internal forces. Design so as to withstand the loads which are going to be added to the beams. Thus the loads which are being added externally are being used in the free body diagrams.

2. Every point on the force vector which is the internal force, is having the same magnitude and the same direction as the whole force vector have.
a) True
b) False

Answer: b [Reason:]s: The vector is made by joining the final and the starting point of the internal force. If we consider any arbitrary point then the length would be calculated w.r.t the starting point, which might give different magnitude but same direction. Thus the answer is false.

3. For getting the normal force on the supports, we do what?
a) Make the vertical sum of the forces equal to zero
b) Make the horizontal sum of the forces equal to zero
c) Make the moment sum of the forces equal to zero
d) Make the rotational sum of the forces equal to zero

Answer: a [Reason:] The making of the vertical force sum zero makes the normal force to be determined. This means that the equilibrium equations when applied at the support gives us the answer. Hence the determination of the normal force is done easily by equating the vertical force sum equal to zero.

4. For getting the horizontal component of the support reactions what do we do?
a) Make the vertical sum of the forces equal to zero
b) Make the horizontal sum of the forces equal to zero
c) Make the moment sum of the forces equal to zero
d) Make the rotational sum of the forces equal to zero

Answer: b [Reason:] The making of the horizontal force sum zero makes the horizontal force to be determined. This means that the equilibrium equations when applied at the support gives us the answer. Hence the determination of the horizontal force is done easily by equating the horizontal force sum equal to zero.

5. Twisting moment is also called as __________
a) Moment of line
b) Moment of section
c) Moment of plane
d) Torsional moment

Answer: d [Reason:] The twisting moment is applied at the point where the couple moment is being applied or is made by the external forces. This makes the formation of the twisting moment along the beam, or the torsional moment. Thus the name twisting or the torsional moment.

a) Centroid
b) Symmetrical centre
c) Rotational centre
d) Chiral centre

Answer: a [Reason:] The loads generally are applied on the centroid of the body. The moment of the body is also calculated along the centroid axis, thus the forces which are acting externally are always acting upon the centroid of the body. Gravity too is acted upon the centroid of the body.

7. The area of does make the difference in the internal forces, that is if the area is large the internal force acting is also large and vice versa.
a) True
b) False

Answer: b [Reason:] This is because the internal forces are independent of the area. They are applied irrespective of the area given to the beams. They are dependent on the external forces. The more the external forces, the more are the internal force. That is the more is the amount of the internal forces.

8. The magnitude of each loading will be ___________ at various points along the axis of the member of the beam.
a) Same
b) Different
c) Slightly different
d) Slightly same

Answer: b [Reason:] The magnitude of each loading will be different on the different points of the beams. The method of section is used to determine these forces. These forces are used so as to make the beams. That is the designing of the beams, the more are the forces than the stronger material is used for the making of the beams.

9. Torsional moment is applied at the ___________ part of the beam.
a) The centroid
b) The left end
c) The right end
d) The axis beyond the body of the beam

Answer: a [Reason:] The torsional moment as said is made to be drawn at the centre of the beam. As it is generated by the various external forces, thus the centroid is the main point of the action of the various forces. Thus the forces which are made to be fallen on the body is having its effect over the centroid of the beam.

10. Normal force is equal to _______________
a) The net horizontal force
b) The net vertical force with a negative sign
c) The net horizontal force with a negative sign
d) The net vertical force

Answer: b [Reason:] The normal force is determined by equating the vertical forces equal to zero. This makes the vertical forces to go on the other side of the equation. Suppose the L.H.S. is having the sum of the vertical forces then the R.H.S. is having the term normal force. That is the normal force is being equated to the negative of the sum of vertical forces.

11. If the normal force creates a tension then the force is said to be ____________
a) Positive
b) Negative
c) Rotational
d) Collinear

Answer: a [Reason:] If the normal forces are giving tension to the body of the beam then the forces are said to be positive. That is if the normal force is making the tension to develop in the beam then it is considered to be positive. This is the basic sign convection that is being used to make the calculations easy.

12. If the shear force creates a clockwise rotation then the force is said to be ____________
a) Positive
b) Negative
c) Rotational
d) Collinear

Answer: a [Reason:] If the shear forces are giving clockwise rotation to the body of the beam then the forces are said to be positive. That is if the shear force is making the beam to develop in the forces that tend to rotate it clockwise then it is considered to be positive. This is the basic sign convection that is being used to make the calculations easy.

13. If the bending of the beam is concave upwards then the bending moment developed is called __________ moment.
a) Positive
b) Negative
c) Rotational
d) Collinear

Answer: a [Reason:] If the bending moment is giving concave bending upward to the body of the beam then the moment are said to be positive. That is if the bending moment is making the beam to develop in the forces that tend to bend the beam concave upward then it is considered to be positive. This is the basic sign convection that is being used to make the calculations easy.

14. 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.

15. Find the tension in the cable AC.

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