Vector and Equilibrium, Representation of a Vector, Subtraction of Vectors, Orthogonal unit vectors, Position Vectors.
Physics vectors and equilibrium form the basis of mechanics, and it is very important in the perspective of the ECAT entry test. To study physical quantities possessing both magnitude and direction, we always use a mathematical concept called vectors. This covers forces, displacement, velocity, and acceleration. Equilibrium, on the other hand, is the study of systems at rest with no net motion due to all forces being balanced. Problem-solving in physics requires a conceptual understanding of these.
Vectors in Physics
A vector is a quantity that requires both magnitude and direction for its complete description. Unlike scalars, which have only magnitude, vectors obey specific mathematical rules. The representation of a vector can be done in multiple ways:
- Graphically: Using directed line segments.
- Symbolically: Denoted by bold letters or letters with an arrow above them.
- Mathematically: Expressed using Cartesian coordinates, such as A = xi + yj + zk.
Vectors can be added or subtracted using the head-to-tail method or by breaking them into rectangular components. The subtraction of vectors is performed by adding the negative of a vector, meaning the direction is reversed before addition.
Equilibrium in Physics
Equilibrium refers to a state in which a body remains at rest or moves with constant velocity. There are two main types of equilibrium:
- Static Equilibrium: A system where all forces cancel each other out, and the body remains stationary.
- Dynamic Equilibrium: A system where a body moves with constant velocity, experiencing no acceleration.
For an object to be in equilibrium, the following conditions must be met:
- The sum of all forces acting on the object must be zero (ΣF = 0).
- The sum of all torques about any axis must also be zero (Στ = 0).
Unit Vectors and Position Vectors
Unit vectors are fundamental in defining vector direction and are represented as î, ĵ, and k̂ along the x, y, and z axes, respectively. The position vector describes a point’s location relative to an origin, helping determine displacement between two points. If two points A and B have coordinates (x₁, y₁, z₁) and (x₂, y₂, z₂), the displacement vector is given by: r = (x₂ – x₁)î + (y₂ – y₁)ĵ + (z₂ – z₁)k̂
Entry Test Physics Vectors and Equilibrium MCQS Online Preparation Sample Paper 1 Questions with Answer
1. How many vectors can be represented
- All of these correct
- Bold letter
- Arrow over the capital letter
- Graphically
2. The minimum number of unequal forces whose vector sum is zero must be?
- 2
- 1
- 3 correct
- 5
3. If the line of action of the force passes through the axis of rotation then the torque is?
- Maximum
- Counterclockwise direction
- Clockwise in direction
- Zero correct
4. Vectors are those physical quantities which require
- Magnitude and direction correct
- Direction
- None of these
- Magnitude
5. Multiplication of a vector is carried out by a
- Direction
- Number correct
- None of these
- Number and direction
6. The positions of two airplanes at any instant are A (2,3,4) and B (5, 6, 7) from the origin in km. Find the distance between the two airplanes.
- 5.2 Km correct
- 3.2 Km
- 4.9 Km
- 5.0 Km
7. When two axes are drawn right to each other are called:
- All of these correct
- Coordinate axes system
- Rectangular coordinate system
- Cartesian system
8. A component of a vector has its?
- Effective value
- B and C
- Normal value
- Given direction correct
9. Vector subtractions are made when vectors are just
- Added
- None of these
- Only make it negative
- First, make it negative then add correct
10. The coordinate axes are those in which lines are drawn
- All of these correct
- Parallel
- Perpendicular
- At right angle
11. A negative of vector can be made when Magnitude is made negative
- Only directions are changed correct
- None of these
- Directions are reversed with negative
- The direction is reverse with a negative magnitude
12. Given A = 2i – 2j + K the magnitude of this vector is?
- 1
- 5 correct
- 2
- 3
13. The component of a vector has its direction as?
- Opposite
- Perpendicular correct
- Same
- None of these
14. For a vector A?
- A.A = 0
- A = A2
- A = 1
- A = A correct
15. The unit vectors are not restricted to Cartesian coordinate systems only.
- None of these correct
- Specific direction
- Any direction
- Not a and b
16. The vector product is?
- Additive
- Anticommutative correct
- Associative
- Commutative
17. Rectangular components are those which are
- Perpendicular to each other
- Right angle to each other
- All of these correct
- Making an angle of 90⁰ with each other
18. Position vector is a vector, which describes the?
- Location of a point with respect to any point
- Location of a point with respect to some related point
- None of these
- Location of a point with respect to origin correct
19. An axes which are at a right angle to both X and Y axes and direction is in space is called:
- Zero vector axis
- Z-axis correct
- None of these
- Unit vector axis
20. A position vector is a vector that is drawn.
- From one point to another
- None of these
- Always from origin to that point
- From the origin to that point correct
Entry Test Physics Vectors and Equilibrium MCQS Online Preparation Sample Paper 2 Questions with Answer
1. The cross product of two perpendicular vectors has magnitude?
- Minimum value
- Zero
- Maximum value correct
- None of these
2. The magnitude of the scalar product is
- AB sin Ѳ
- AB
- AB cos Ѳ correct
- None of these
3. In right-hand rule, the direction of the product vector will be?
- Along the rotation of fingers
- Perpendicular to the erect thumb
- Along the erect thumb correct
- None of these
4. The vector sum of three vectors gives a zero resultant. What can be the orientations?
- 90⁰
- 120⁰ correct
- 180⁰
- 60⁰
5. The cross product of parallel vectors is zero when the angle between?
- Ѳ = 90⁰
- A and C correct
- Ѳ = 0⁰
- Ѳ = 180⁰
6. Is it possible to add a vector quantity to a scalar quantity?
- None of these
- No
- Never correct
- Yes
7. How many multiplications of vectors are there?
- 2 correct
- None of these
- 1
- 3
8. The cross-product of parallel vectors has a magnitude
- Zero correct
- Minimum value
- None of these
- Maximum value
9. Under what circumstance would a vector have components that are equal in magnitude?
- 135⁰, 225⁰
- None of these
- 45⁰, 145⁰, 245⁰
- 45⁰, 135⁰, 225⁰ and 315⁰ correct
10. Vector A lies in the XY plane. For what orientation with both of its rectangular components be negative?
- None of these
- I-quadrant
- III-quadrant correct
- II-Quadrant
11. When the vectors are mutually perpendicular then their scalar product is?
- Zero correct
- Maximum
- Minimum
- None of these
12. Vector A lies in the XY plane. For what orientation will its components have opposite signs?
- A and C correct
- II-quadrant
- IV-quadrant
- III-quadrant
13. The self-product of two vectors in cross-product is?
- None of these
- Zero correct
- Only same vector
- Square of vector
14. Can a vector have a component greater than the vector’s magnitude?
- Yes is some cases
- None of these
- No
- Yes correct
15. Can the magnitude of a vector have a negative value?
- None of these
- Yes
- Yes is some cases
- No correct
16. Find the angle between two forces of equal magnitude of their resultant is also equal to the magnitude of either of these forces.
- 180⁰
- 120⁰ correct
- 360⁰
- 60⁰
17. The position of two airplanes at any instant is at A (2, 3, 4) and B (5, 6, 7) from the origin in km. Find the distance between the two airplanes.
- 5.0 Km
- 5.2Km correct
- 4.9Km
- 3.2Km
18. The magnitude of the scalar Product can also written as?
- None of these
- The magnitude of vector and effective component of the vector correct
- Vector and perpendicular component of vice vector
- vector and effective component of the vector
19. The self-product of the vector is equal to
- Vector
- Zero
- The square of the vector correct
- None of these
20. If one of the rectangular components of a vector is not zero, can its magnitude be zero?
- It is zero
- It is not Zero correct
- None of these
- It may be negative
Entry Test 2021 Physics Vectors and Equilibrium MCQS Online Preparation Sample Paper 3 Questions with Answer
1. The magnitude of i² in the scalar product is?
- Zero
- 1 correct
- Less than 1
- Greater than 0
2. Can a body rotate about its center of gravity under the action of its weight?
- Both
- Yes
- None of these
- No correct
3. The magnitude of j² in cross-product is?
- Zero correct
- Greater than 1
- 1
- Less than 0
4. Rectangular components of a vector are those that have an angle between them.
- 0⁰
- 60⁰
- 90⁰ correct
- 30⁰
5. A body in equilibrium implies that it is not moving nor rotating.
- Sometimes is equilibrium
- False correct
- None of these
- True
6. How would the two vectors of the same magnitude have to be oriented, if they were to be combined to give a result equal to a vector of the same magnitude?
- 270⁰
- None of these
- 60⁰
- 120⁰ correct
7. Torque is zero if
- The body is at rest
- Uniform angular acceleration
- Moment arm is zero correct
- None of these
8. In torque when the force is kept constant and the moment arm increases, then the torque?
- Increases correct
- None of these
- Remains constant
- Decreases
9. The SI units of torque are?
- Nm²
- Nm¯²
- Nm¯¹
- Nm correct
10. Torque is a physical quantity which is?
- Scalar quantity
- Constant quantity
- None of these
- Vector quantity correct
11. Two vectors have unequal magnitudes can their sum be zero?
- Can be zero
- No
- Yes correct
- None of these
12. The direction of torque is?
- Perpendicular plan formed by F and r correct
- Along F
- None of these
- Along r
13. If we keep the moment arm, fixed while changing the force, then, the torque is?
- None of these
- Somewhat change
- Changed correct
- Does not change
14. The perpendicular distance from the axis of rotation to the line of the action of force is called?
- Linear distance
- None of these
- Angular distance
- Momentum arm correct
15. The magnitude of work is zero when the angle between force and displacement is:
- 10⁰
- None of these
- 90⁰ correct
- 0⁰
16. Can you add zero to a null vector?
- None of these
- No correct
- Yes
- Yes is some cases
17. Torque is the turning effect of a?
- Force correct
- None of these
- Body
- Momentum
18. If coplanar forces acting on a body form a closed polygon, then the body is said to be in equilibrium.
- False correct
- Yes
- None of these
- Sometimes is equilibrium
19. The direction of torque can be determined by?
- Left-hand rule
- None of these
- Head-to-tail rule
Right-hand rule correct
Conclusion
This is where Physics Vectors and Equilibrium help us with working with many different problems in the ECAT entry test. Reviewing the basics of vector operations to equilibrium conditions mastering these concepts will significantly enhance problem-solving skills. Just keep doing MCQs you will get the concept and improve your accuracy in solving entry-test physics questions.