Moment of A Force - Free MCQ Practice Test with solutions, GATE Civil Engineering

1. Find the moment produced by the 75 N force about P

   • The bar is 3 m long at 60° above horizontal, and the 75 N force is vertical.

   • The horizontal lever arm from P to R is:

     d = 3 * cos(60°) = 3 * 0.5 = 1.5 m

   • So the moment is:

     M = 75 N * 1.5 m = 112.5 N·m

2. Determine the smallest force at R producing the same moment

   • The maximum moment arm you can get at R is if you apply the force perpendicular to the bar, giving a lever arm of the full 3 m.

   • To reproduce M = 112.5 N·m with lever arm 3 m, you need:

     F = M / 3 m = 112.5 / 3 = 37.5 N

So the smallest force is 37.5 N.

The moment of the force measures the tendency of the rotation of the body along any axis, whether it be the centroid axis of the body, or any of the outside axis. The couple moment is produced by two forces, not by a single force. The total work done is the dot product of force and distance not the cross.

The correct answer is a) It is heading inwards, i.e. the direction is towards the inside of the car.

Here is a step-by-step explanation:

1. Understanding the "Moment": The question refers to the "moment of the moment caused by the rotation of the tires." In physics, this is best interpreted as the angular momentum of the tires. Angular momentum is a vector quantity, meaning it has both a magnitude and a direction.

2. The Right-Hand Rule: To find the direction of the angular momentum vector for a rotating object, you can use the right-hand rule. Curl the fingers of your right hand in the direction of the object's rotation. Your thumb will then point in the direction of the angular momentum vector.

3. Applying the Rule to a Car Tire:

   • Imagine a car moving forward. The tops of the tires are rotating in the forward direction.

   • For the tires on the right side of the car (passenger side in the US): When viewed from the outside, the wheel rotates in a counter-clockwise direction. If you curl the fingers of your right hand counter-clockwise, your thumb points to the left, which is inward toward the center of the car.

   • For the tires on the left side of the car (driver side in the US): When viewed from the outside, the wheel rotates in a clockwise direction. If you curl your fingers in a clockwise direction, your thumb points to the right, which is also inward toward the center of the car.

In both cases, the angular momentum vector for a rotating tire on a car moving forward points along the axle towards the car's interior. Therefore, the direction is inwards.

The tendency of rotation of the body along any axis also called the torque. It is the moment of the force acting perpendicular to the direction of the axis of rotation. If the axis and the force are meeting at any point then there is no moment applied by the force.

The moment is the product of the force applied to the body and the perpendicular distance of the point of action of the force to the axis about which the body is being rotated. That is the moment is the cross product of the force and the distance between the axis and the point of action.

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 0m. Thus we get the distance. And hence multiply it with the force, 0x50.

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.

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.

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.

The moment axis, force and the perpendicular distance is lying in the three dimensional Cartesian. It doesn’t lye on the single plane. It also doesn’t lye in a single line. Nor in the direction of the force. Thus they all lye in the planes which are perpendicular to each other.

As the curling will give the direction perpendicular to the paper. But it does depend upon the rotation sense. In this example, the sense is clockwise. Thus the thumb goes into the paper. That is it goes away from the viewer. Thus the answer.

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. Thus assumptions cant be taken for the direction of the moment.

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 7m. Thus we get the distance. And hence multiply it with the force, 7×50

= 350 Nm.

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 a 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

= 100Nm

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.

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.