Answer: a [Reason:] When you will resolve the vector in its x, y and z-axis components, you will get an equation containing cosα. After getting the correctly, you need to directly put that value in the previous equation of components.

Answer: b [Reason:] Just add the two vectors in their Cartesian form only. After that you will get the resultant vector in the Cartesian form. After that just divide the y-axis component’s magnitude by the resultant of the vector. You will get cosβ.

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.

Answer: b [Reason:] 122 + 82 + 242 = 282 . After you get this, the 28 is the magnitude. This is the using of distance formula between two Cartesian points. Considering the point (12, -8, -24) and then calculating the distance from the origin.

Answer: a [Reason:] First subtract the coordinates of the A form B. And place the x, y and z-axis coordinate separated by i, j and k respectively. Like Ai + Bj + Ck , if A, B and C are the x, y and z-axis coordinates. You will get a Cartesian vector, just find its magnitude and divide it with the vector.

Answer: a [Reason:] First try to make the unit vector of AB. Then you will get the Cartesian form of unit vector, after that just multiply 750 scalar quantity with it. Which means you are first taking out the desired direction and then multiplying the scalar to get the desired vector in desired direction.

Answer: d [Reason:] Just make the unit vectors of the given directions of the vectors and then multiply them with their respective magnitudes, after than you will get two vectors in the Cartesian form. Just add them.

Answer: d [Reason:] It’s a calculative question, but still can be solved if you construct the triangle of the respective cosine inverses given, then convert them in the tangent form then use log table, if necessary. Or use of calculator is also good if permissible. Or you can make use of triangle laws to obtain the same.

Answer: a [Reason:] Yes, whenever two vectors are there, they are always in a single plane. If the emerging vectors are more than three then saying about their plane is somewhat difficult. But for two vectors it seems easy to understand about their plane.

Answer: b [Reason:] Yes, whenever two vectors are there, they are always in a single plane. But you cannot say about the three vectors, they may or may be. Because if the emerging vectors are more than three then saying about their plane is somewhat difficult. But for two vectors it seems easy to understand about their plane.

Answer: c [Reason:] The magnitude of the unit vector is always = 1. This means unit vector is the vector in the direction of the original vector and the magnitude of the same is unity. And unit vector is always in the direction of its vector.

Answer: d [Reason:] As position vector defines the position of the point in the Cartesian plane wit respect of the origin, it will definitely have a direction and also a magnitude. Unit vector is a vector whose magnitude is = 1 and is having a specific direction.

Answer: b [Reason:] The magnitude of the unit vector will change by the amount of the scalar multiplied. Not the direction. Because the direction is being fixed after the application of the unit vector’s calculation. That is the vector divided by its magnitude.

Answer: b [Reason:] We find the vector form from subtracting the initial position coordinates from final position coordinates. Not from subtracting the final position coordinates from initial position coordinates.

Answer: c [Reason:] All vectors have three components, whether they are zero or not. And unit vector is always in the direction of its vector. And the unit vector has the magnitude equal to unity. This means unit vector is the vector in the direction of the original vector and the magnitude of the same is unity.

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.

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.

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.

Answer: a [Reason:] For solving of the unknown tension in the belts, T₂ = T₁e^µB equation is used. In this the R.H.S tension is the maximum tension of the two tensions. While the other one is the smaller one. And the µ is coefficient of friction between the belt and the surface. And the B is the angle of belt to the surface in radians.

Answer: b [Reason:] The dry friction is acted upon the surfaces. Whatever may be the surfaces. And they are tangential to each other. As we know the friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. The dry friction is also termed as the Coulomb friction as it was given by C.A. Coulomb.

Answer: a [Reason:] As the loads are being acting in the downward direction. Thus to make the forces balance, the normal forces act in the vertically upward direction. As we know that when there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. This friction magnitude is taken out from these normal forces.

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.

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.

Answer: d [Reason:] The net forces acting on the body is shown by the help of the resultant forces. This is because the resultant forces have the sum of all the forces which are acting on the direction which is same. Thus the resultant forces are used to show the net forces acting in the body.

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.

Answer: a [Reason:] The component of the force in the v axis, it is equal to 100cos(15˚). This is the application of the triangle over the figure. Try to resolve the components of the given force. It will be easy. This is one of the simplest example of solving for the forces acting over the belts.

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. Vector math is unchanged throughout.

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.

Answer: a [Reason:] For solving of the unknown tension in the belts, T2 = T1eµB equation is used. In this the R.H.S tension is the maximum tension of the two tensions. While the other one is the smaller one. And the µ is coefficient of friction between the belt and the surface.

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.

Answer: d [Reason:] The journal bearings are being used in the supports. They are used as to support the loadings. This means that the more the bearings the more is the stable the structure. Thus the use of journal bearings.

Answer: b [Reason:] The dry friction is acted upon the surfaces. And they are tangential to each other. As we know the friction is the phenomena that defines that there is a resistance which is present there between the two surfaces. This Coulomb friction is also known as dry friction.

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.

Answer: a [Reason:] When there is no lubricating fluid present between the surfaces in contact, the dry friction occurs. Thus as the name suggests, dry friction. When there is no liquid present over there the surfaces are going to be said dry only. Thus the term dry friction.

Answer: d [Reason:] We first make the free body diagram of journal bearings 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.

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.

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.

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.

Answer: a [Reason:] The basic types of the motion of the body are translation and rotational. In which translation means the motion is a straight motion while the in the rotational motion the body is moving of the body along the axis. The pivots do circular motion.

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.

Answer: b [Reason:] The coplanar forces can be easily simplified in the simplification of the force and couple system. This is not only for the coplanar system of the forces, but for any of the dimension vector. Which means the answer is false.

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.

Answer: a [Reason:] We can take such assumptions. We are free to do so. We just need to specify if clockwise is positive then the counter clockwise is to be negative. Also such assumption are very useful in 2D calculation of the moments caused by various forces on the body.

Answer: a [Reason:] As the moment is the product of the force and the perpendicular distance of the point of action and the axis, thus more the distance more will be the moment. And hence to overcome that you have to apply more energy. Thus the answer.

Answer: a [Reason:] When we consider about the dimensions we need to be careful. The moment is the vector quantity. Thus the value of the total moment caused by various forces acting on the body is the vector sum of all the vectors. Also the moments are not perpendicular to each other, unless it is specified.

Answer: a [Reason:] The screws are generally used as the fasteners. The main thing about the screws is that the friction helps the holding of the structures. Also screws help make the structure join fast and efficiently. Thus the name fasteners.

Answer: a [Reason:] The square threaded screws are used in the machines. As the screws are generally used as the fasteners. The main thing about the screws is that the friction helps the holding of the structures. Also screws help make the structure join fast and efficiently.

Answer: a
Answer: The square threaded screws are used in the machines. As these screws are generally used as the fasteners. The main thing about these screws is that the friction helps the holding of the structures. Also screws help make the structure join fast and efficiently. And in these screws forces act along the axis of screws.

Answer: a [Reason:] The angle of the threading in the screw is determined by inverse tangent trigonometric function. This is the generalised form of the function which is being used so as to get the value of the angle. In wedges the same function is used so as to find the angle of wedge.

Answer: a [Reason:] The angle of the threading in the screw is determined by inverse tangent trigonometric function. This is the generalised form of the function which is being used so as to get the value of the angle. In wedges the same function is used so as to find the angle of wedge. And in both the case the ratio is the vertical is to horizontal.

Answer: a [Reason:] The angle of the threading in the screw is determined by inverse tangent trigonometric function. This is the generalised form of the function which is being used so as to get the value of the angle. In wedges the same function is used so as to find the angle of wedge. And thus the horizontal distance is called as lead.

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.

Answer: b [Reason:] As we know that the moment is the cross product of the distance and the force we will try to apply the same here. We see that the perpendicular distance is 1.5 (3cos60). Thus we get the distance. And hence multiply it with the force, 75×1.5. Because the force component perpendicular to the distance need to be taken.

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.

Answer: b [Reason:] The forces in the three force system are 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.

Answer: c [Reason:] The couple moment depends only on the distance vector between the forces. The radius vector of the forces are not making the couple depended over it. But the distance vector is driven by subtracting the radius vectors of the forces. This means that, moment of the couple doesn’t directly depend on the radius vector of forces.

Answer: c [Reason:] The forces are always in the opposite direction for the couple moment. But if they don’t act like the same that is they change their directions and align themselves in the same direction then the couple is not possible.

Answer: a [Reason:] The equilibrium is only attained if the net force on the body tends to be equal to zero. Thus the forces cancel 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.

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.

Answer: a [Reason:] As we know that the moment is the cross product of the distance and the force we will try to apply the same here. We see that the perpendicular distance is 3m. Thus we get the distance. And hence multiply it with the force, the moment = 112.5Nm. Because the force component perpendicular to the distance need to be taken.

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

Answer: a [Reason:] The determination of the internal forces is done by various methods among which the method of section is the one. Also we have method of joints, which is done so as to determine the internal forces which are being developed in the trusses or the frames. This is done as to design them.

Answer: b [Reason:] In method of sections the determination of the forces is done over the trusses or the beams. It is not done on the joints. But yes the joints are used as the forces acting on the joints are used in the calculations. This is again used for the designing of the beams.

Answer: d [Reason:] The free body diagram is using the external forces which are acting on the beam as the main purpose is to design the beam. 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.

Answer: b [Reason:] In method of sections the determination of the forces is done over the trusses or the beams. It is not done on the joints. But yes the joints are used as the forces acting on the joints are used in the calculations. This is again used for the designing of the beams.

Answer: c [Reason:] The forces which are acting perpendicular to the body of the beams are called as the normal forces. These are the forces which are supporting the beam. These forces are being calculated by the help of equilibrium equations. Thus the forces which are perpendicular to the surface are the normal forces.

Answer: c [Reason:] The forces which are acting tangentially to the body of the beams are called as the shear forces. These are the forces which are giving moment to the beams. These forces are being calculated by the help of equilibrium equations. Thus the forces which are parallel to the surface are the shear forces.

Answer: d [Reason:] The forces are making the body tend to rotate. This is in general making the body rotate or make generate the moment in the beams. This moment is the same thing as the couple moment. But in beams it is referred as bending moment. And is again used for the designing of beams.

Answer: a [Reason:] The force components are the forces which are the ones which prevents the beam from relative translation. This means that the shearing generated will be held strongly by the help of the forces generated. The main motto is to make the beam stable and don’t allow the relative translation occur.

Answer: b [Reason:] The couple moments are the moments which are the ones which prevents the beam from relative rotation. This means that the rotation generated will be held strongly by the help of the opposite moments generated. The main motto is to make the beam stable and don’t allow the relative rotation to occur.

Answer: c [Reason:] As the law state that there is always a reaction to every action applied. Thus if the forces are applied at the section of the beams, i.e. the external forces than there must be reactive forces. And these reactive forces act in opposite directions of the forces which are being applied externally.

Answer: a [Reason:] The determination is usually done in this manner only. The selection is done as by selecting the one having one unknown and two known forces. This will ensure that the unknown value will be found. And also we have less number of unknowns which are needed to be founded.

Answer: d [Reason:] For the equilibrium in beams by considering any of the 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. Thus the conditions for the equilibrium of the beams.

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

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