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

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

Answer: b [Reason:] The collar bearings and pivots are being used in the machines. They are used as to support the loadings. This means that the more the collar bearings or pivots more is the stable the structure. Thus used as a supporting system to the shafts.

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:] 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 collar bearings or pivots 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: a [Reason:] The cross product of two vectors give 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. The cross product is same for all the systems of its application.

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. The vector math system remains same for every system in the environment.

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: b [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: 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 force developed by a support doesn’t allow the translation of its attached member. This is the basic condition for the equilibrium of the forces in any dimension. This rule is applied when the support reactions are taken into the account for the equilibrium of the body.

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.

Answer: b [Reason:] The development of the couple moment is when there is prevention of the rotation of the attached member. This is the basic condition for the equilibrium of the couple moments in any dimension. This rule is applied when the couple moments are taken into the account for the equilibrium of the body.

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: 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.

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.

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.

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.

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.

Answer: c [Reason:] The experiments have founded that the single pin, single bearing and single hinge resist both force and couple moments. This does helps in attaining the equilibrium of the body. Thus proper guiding must be taken during solving the question on the same.

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

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.

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.

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

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 5m. Thus we get the distance. And hence multiply it with the force, 5x2000xsin30. Because the force component perpendicular to the distance need to be taken.

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. So let the distance be y, then the force of 200N will act downward. The distance perpendicular is xcos60. Thus equating the 112.5 to 200ycos60.

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. But here we have number of forces components acting on the T point. So by adding all the moments caused by all the forces will give us the value as 600Nm.

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: 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: 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.

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

Answer: c [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 2m. Thus we get the distance. And hence multiply it with the force, 2×50.

Answer: a [Reason:] The moments in the 2D can be added algebraically just like the scalar quantities. But the need is that the signs must be taken into the consideration. As if clockwise is positive, so anti clockwise is negative. And the result can be negative too. That is counter clockwise direction.

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

Answer: c [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. But here we have number of forces components acting on the T point. So by adding all the moments caused by all the forces will give us the value as 0Nm.

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 3sin60. Thus we get the distance. And hence multiply it with the force, moment = 112.5Nm. Because the force component perpendicular to the distance need to be taken.

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: b [Reason:] The moment axis is always perpendicular to the planes of the force and the distance of the axis and the point of action of the force on the body. This means that the moment is the cross product of the force and the distance between the axis and the point of action of the force.

Answer: a [Reason:] The Pascal law states that the liquid at rest applies pressure at a point is same in all directions. This means that the pressure is there in spite of the direction. And it is present in the same direction and is having same magnitude.

Answer: a [Reason:] The Pascal law states that the liquid at rest applies pressure at a point is same in all directions. This means that the pressure is there in spite of the direction. And it is present in the same direction and is having same magnitude.

Answer: d [Reason:] The Pascal law states that the liquid at rest applies pressure at a point is same in all directions. This means that the pressure is there in spite of the direction. And it is present in the same direction and is having same magnitude.

Answer: b [Reason:] The liquid must be incompressible. The Pascal law states that the liquid at rest applies pressure at a point is same in all directions. This means that the pressure is there in spite of the direction.

Answer: a [Reason:] The liquid must be incompressible. The Pascal law states that the liquid at rest applies pressure at a point is same in all directions. This means that the pressure is there in spite of the direction. But the gases are compressive that’s why it is not used in the gas form.

Answer: a [Reason:] The pressure is always acted normal to the surface of the body. Thus the pressure plays a role as a vector in this case. So mainly the pressure must be considered as normal to the surface of the body.

Answer: a [Reason:] The body used in the determination of the fluid pressure equations is immersed in the liquid. It is completely immersed in the liquid. So as to make the calculations of the pressure beneath the liquid.

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:] 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.

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: 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.

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.

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.

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.

Answer: a [Reason:] The Pascal law states that the liquid at rest applies pressure at a point is same in all directions. This means that the pressure is there in spite of the direction. And it is present in the same direction and is having same magnitude.

Answer: a [Reason:] Frames and machines are two types of structural figures which are often made of pin connected multi-force members. That is more than two forces are subjected over the machines. Thus the term multi-force is used for the frames and the machines.

Answer: a [Reason:] The frames are used as support for the structures. They hold up the structure into the right place. They are made for holding up the structures in the place. They also provide the stability to the structure.

Answer: b [Reason:] The machines are designed such that they can transmit the effects of forces. Thus making the free body diagrams of the various joints and doing the calculations makes us determine the various reaction values. And for the asked reaction equating the forces acting equal to zero, we get the answer.

Answer: b [Reason:] The machines are designed such that they contain the moving parts. As the machines are made for working in various fields, they are designed as to contain the moving parts. They are also such designed such that the moving parts in are not damaged.

Answer: a [Reason:] The machines are designed such that they can transmit the effects of forces. As the machines are made for working in various fields, they are also such designed so as to alter the effects of the forces. They are also such designed such that the moving parts in are not damaged.

Answer: a [Reason:] The machines are designed such that they can transmit the effects of forces. Thus making the free body diagrams of the various joints and doing the calculations makes us determine the various reaction values. And for the asked reaction equating the forces acting equal to zero, we get the answer.

Answer: a [Reason:] The forces acting on the joints and on the members are determined by the simple equilibrium equations, which are used in the usual beams and trusses. The forces which are acting over the joint of the frames and machines are no more different from the forces acting on the beams and trusses.

Answer: a [Reason:] The forces are determined because the designing of the frames and machines. This is done so as if the forces are applied to frames and the machines, they don’t collapse. Thus the forces acting on the joints and the members are important to be determined.

Answer: a [Reason:] The forces obtained at the joints and the members of the machines are very important. They are used for the designing the size of the members, connections done in the frames and machines. They are obtained by applying the simple equilibrium force equations on the system. Net forces are made to be zero, and the unknowns are determined.

Answer: b [Reason:] There is a great need of the making of the free body diagrams in the calculations of the forces that are being acted upon the joints. This helps in making of the design of the machines and the frames. These are very important quantities that are being determined.

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

Answer: d [Reason:] The machines are designed such that they can transmit the effects of forces. Thus making the free body diagrams of the various joints and doing the calculations makes us determine the various reaction values. And for the asked reaction equating the forces acting equal to zero, we get the answer.

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.

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.

Answer: c [Reason:] The machines are designed such that they can transmit the effects of forces. Thus making the free body diagrams of the various joints and doing the calculations makes us determine the various reaction values. And for the asked reaction equating the forces acting equal to zero, we get the answer.