Vectors and Equilibrium – 100 Basic MCQs with Answers & Explanations | Board & MDCAT Preparation

100 Important MCQs (Level -1) on Vectors and Equilibrium, Physics (Unit-Wise MCQs Practice):

---

👉Physics MCQs Hub – Unit wise Physics MCQs Practice (Main-Page)👈

---

Whether you are preparing for board examinations, chapter tests, college assessments, or competitive entrance exams (MDCAT, ECAT, NUST, PIEAS, GIKI, UET, FAST, and other engineering or medical admission tests), this comprehensive Vectors and Equilibrium MCQ collection is designed to help you master one of the most important topics in Physics. The questions are arranged progressively—from basic concepts to advanced numerical problems and higher-order thinking—ensuring complete and systematic preparation for every type of examination.

This chapter-wise MCQ collection includes:

100 Basic MCQs (1–100) – Covering fundamental concepts of vectors and scalars, Cartesian coordinate system, vector representation, vector addition, vector components, scalar product, vector product, torque, and equilibrium.

100 Advanced & Numerical MCQs (101–200) – Focusing on vector addition using components, resultant vectors, dot product and cross product calculations, torque, moments of force, equilibrium conditions, and numerical problem-solving.

50 Higher-Order Thinking Skills (HOTS) MCQs (201–250) – Designed to strengthen analytical reasoning, conceptual understanding, real-life applications, and problem-solving abilities involving vectors, torque, and equilibrium.

50 Challenging MCQs Quiz with Answers (1–50) – Carefully selected conceptual, numerical, and HOTS questions to strengthen problem-solving skills and prepare students for board and competitive examinations. 

This MCQ collection covers:

• Scalars and vectors
• Cartesian coordinate system
• Representation of vectors
• Head-to-tail rule of vector addition
• Resolution of vectors into perpendicular components
• Resultant of vectors using component method
• Scalar (dot) product of vectors
• Vector (cross) product of vectors
• Right-hand thumb rule for vector product
• Torque (moment of force)
• Applications of torque in daily life
• First condition of equilibrium
• Second condition of equilibrium
• Translational and rotational equilibrium
• Two-dimensional equilibrium problems
• Free-body diagrams and force analysis
• Practical applications of vectors and equilibrium in engineering and mechanics

Every MCQ includes the correct answer along with a clear, concept-based explanation to strengthen understanding, improve analytical thinking, and reinforce the fundamental principles of vectors and equilibrium.

This question bank helps students to:

• Build a strong conceptual foundation in vectors and equilibrium
• Master vector addition and resolution techniques
• Develop confidence in dot product and cross product applications
• Improve numerical and analytical problem-solving skills
• Understand torque and rotational effects of forces
• Apply the first and second conditions of equilibrium effectively
• Solve two-dimensional statics problems systematically
• Avoid common examination mistakes
• Increase speed, accuracy, and confidence in objective-type questions
• Prepare effectively for both board examinations and competitive entrance tests

With 250 carefully selected MCQs arranged into 100 Basic, 100 Advanced & Numerical, and 50 HOTS questions, along with a 50-question Challenging Quiz, this all-in-one Vectors and Equilibrium MCQ Bank provides complete exam preparation. It is an excellent study resource for strengthening concepts, improving problem-solving skills, and achieving outstanding performance in both school examinations and competitive physics entrance tests.

---

Best Budget Laptops for Students for Study, Coding & Office Work 
(2026 Amazon Deals)

👉 Check Today’s Price on Amazon👈

👉 Check Acer Aspire 5 Price on Amazon

👉 Buy Lenovo IdeaPad Slim 3 on Amazon

👉 See HP Pavilion Latest Deal on Amazon

👉 View ASUS Vivobook 16 Details on Amazon

👉 Check MacBook Air Student Price on Amazon

---

Level-I – 100 Basic MCQs (1–100) – Building a Strong Foundation

---

MCQs 1–25: Cartesian Coordinate System, Vector Basics & Introduction to Vector Addition

---

MCQ No. 1

The Cartesian coordinate system consists of:

a. One axis

b. Two mutually perpendicular axes

c. Three parallel axes

d. Four axes

Correct Answer: b. Two mutually perpendicular axes

Explanation:
The Cartesian coordinate system consists of two mutually perpendicular axes: the X-axis (horizontal) and the Y-axis (vertical). These axes intersect at the origin and are used to locate points and represent vectors in a plane.

---

MCQ No. 2

The point where the X-axis and Y-axis intersect is called the:

a. Vertex

b. Origin

c. Midpoint

d. Pole

Correct Answer: b. Origin

Explanation:
The point (0, 0), where the X-axis and Y-axis meet, is known as the origin. It serves as the reference point for measuring the coordinates of all points and vectors.

---

MCQ No. 3

In the Cartesian coordinate system, the X-axis is:

a. Vertical

b. Horizontal

c. Circular

d. Inclined

Correct Answer: b. Horizontal

Explanation:
The X-axis is drawn horizontally and represents the horizontal direction, while the Y-axis is drawn vertically.

---

MCQ No. 4

In the Cartesian coordinate system, the Y-axis is:

a. Horizontal

b. Circular

c. Vertical

d. Inclined

Correct Answer: c. Vertical

Explanation:
The Y-axis is perpendicular to the X-axis and represents the vertical direction.

---

MCQ No. 5

If both $R_x$ and $R_y$  are positive, the vector lies in the:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Correct Answer: a. First quadrant

Explanation:
A vector having both positive X and positive Y components lies in the first quadrant.

---

MCQ No. 6

If $R_x$ is negative and $R_y$ is positive, the vector lies in the:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Correct Answer: b. Second quadrant

Explanation:
A negative X-component and a positive Y-component indicate that the vector lies in the second quadrant.

---

MCQ No. 7

If both $R_x$ and $R_y$ are negative, the vector lies in the:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Correct Answer: c. Third quadrant

Explanation:
When both X and Y components are negative, the vector is located in the third quadrant.

---

MCQ No. 8

If $R_x$  is positive and $R_y$ is negative, the vector lies in the:

a. First quadrant

b. Second quadrant

c. Third quadrant

d. Fourth quadrant

Correct Answer: d. Fourth quadrant

Explanation:
A positive X-component and a negative Y-component place the vector in the fourth quadrant.

---

MCQ No. 9

If $R_x = 0$  and $R_y \neq 0$ , the vector lies on the:

a. X-axis

b. Y-axis

c. Origin

d. First quadrant

Correct Answer: b. Y-axis

Explanation:
When the X-component is zero, the vector acts entirely along the Y-axis.

---

MCQ No. 10

If $R_y = 0$  and $R_x \neq 0$ , the vector lies on the:

a. X-axis

b. Y-axis

c. Origin

d. Second quadrant

Correct Answer: a. X-axis

Explanation:
When the Y-component is zero, the vector acts entirely along the X-axis.

---

MCQ No. 11

A vector is a physical quantity that possesses:

a. Magnitude only

b. Direction only

c. Both magnitude and direction

d. Neither magnitude nor direction

Correct Answer: c. Both magnitude and direction

Explanation:
A vector is completely described by both its magnitude and its direction. Examples include force, displacement, and velocity.

---

MCQ No. 12

Which one of the following is a vector quantity?

a. Mass

b. Temperature

c. Time

d. Force

Correct Answer: d. Force

Explanation:
Force has both magnitude and direction; therefore, it is a vector quantity. Mass, time, and temperature are scalar quantities.

---

MCQ No. 13

Which one of the following is a scalar quantity?

a. Velocity

b. Force

c. Displacement

d. Distance

Correct Answer: d. Distance

Explanation:
Distance has magnitude only and no direction; therefore, it is a scalar quantity.

---

MCQ No. 14

A unit vector is a vector whose magnitude is:

a. 0

b. 1

c. 2

d. Depends on direction

Correct Answer: b. 1

Explanation:
A unit vector has a magnitude of one and is used only to indicate direction.

---

MCQ No. 15

The primary purpose of a unit vector is to represent:

a. Magnitude only

b. Direction only

c. Mass

d. Work

Correct Answer: b. Direction only

Explanation:
A unit vector indicates only the direction of a vector without changing its physical nature.

---

MCQ No. 16

The rectangular components of a vector are always:

a. Parallel

b. Perpendicular

c. Equal

d. Opposite

Correct Answer: b. Perpendicular

Explanation:
A vector is resolved into two mutually perpendicular (rectangular) components along the X-axis and Y-axis.

---

MCQ No. 17

The process of splitting a vector into two mutually perpendicular components is called:

a. Vector addition

b. Vector multiplication

c. Resolution of vectors

d. Vector projection

Correct Answer: c. Resolution of vectors

Explanation:
Resolution of vectors is the process of expressing a vector in terms of its horizontal and vertical components.

---

MCQ No. 18

Resolution of a vector is the reverse process of:

a. Vector multiplication

b. Vector addition

c. Vector subtraction

d. Scalar multiplication

Correct Answer: b. Vector addition

Explanation:
Vector addition combines components to produce a resultant vector, while resolution separates a vector into its components.

---

MCQ No. 19

Two vectors can be added only when they have:

a. Different units

b. Different physical meanings

c. The same physical quantity and the same unit

d. Equal magnitudes only

Correct Answer: c. The same physical quantity and the same unit

Explanation:
Only vectors representing the same physical quantity and expressed in the same unit can be added or subtracted.

---

MCQ No. 20

The resultant of two or more vectors is obtained by:

a. Multiplication

b. Division

c. Vector addition

d. Differentiation

Correct Answer: c. Vector addition

Explanation:
The resultant vector represents the combined effect of two or more vectors and is obtained by vector addition.

---

MCQ No. 21

The head-to-tail method is primarily used to determine:

a. Vector subtraction

b. Vector multiplication

c. Vector addition

d. Scalar multiplication

Correct Answer: c. Vector addition

Explanation:
The head-to-tail rule is a graphical method used to find the resultant of two or more vectors.

---

MCQ No. 22

The head-to-tail rule of vector addition is also known as the:

a. Triangle law of vector addition

b. Polygon law of vectors

c. Right-hand rule

d. Parallelogram theorem

Correct Answer: a. Triangle law of vector addition

Explanation:
When two vectors are added by placing the tail of one vector at the head of the other, the method is known as the triangle law of vector addition.

---

MCQ No. 23

The parallelogram law is used to determine the:

a. Product of two vectors

b. Difference of vectors

c. Resultant of two vectors acting simultaneously

d. Magnitude of a scalar quantity

Correct Answer: c. Resultant of two vectors acting simultaneously

Explanation:
The parallelogram law provides a graphical method for determining the magnitude and direction of the resultant of two vectors acting at the same point.

---

MCQ No. 24

The polygon law of vector addition is an extension of the:

a. Parallelogram law

b. Triangle law

c. Dot product

d. Cross product

Correct Answer: b. Triangle law

Explanation:
The polygon law extends the triangle law to determine the resultant of more than two vectors.

---

MCQ No. 25

Which of the following statements about vector addition is correct?

a. Only vectors with the same physical quantity and unit can be added.

b. Any two physical quantities can be added as vectors.

c. Scalars can always be added to vectors.

d. Vectors can only be added if they have equal magnitudes.

Correct Answer: a. Only vectors with the same physical quantity and unit can be added.

Explanation:
Vector addition is meaningful only when the vectors represent the same physical quantity and are expressed in the same unit. For example, force can be added to force, but force cannot be added to displacement.

---

MCQs 26–50: Resolution of Vectors & Addition Using Perpendicular Components

---

MCQ No. 26

A vector resolved into rectangular components is expressed along the:

a. Parallel axes

b. Perpendicular axes

c. Circular axes

d. Inclined axes

Correct Answer: b. Perpendicular axes

Explanation:
A vector is resolved into two mutually perpendicular components, usually along the X-axis and Y-axis.

---

MCQ No. 27

The horizontal component of a vector of magnitude A making an angle θ with the positive X-axis is:

a. $A\sin \mathrm{\theta }$

b. $A\tan\theta$ 

c. $A\cos\theta$ 

d. $A\cot\theta$ 

Correct Answer: c. $A\cos\theta$ 

Explanation:
The horizontal (X) component of a vector is given by:

$$A_x=A\cos\theta$$

---

MCQ No. 28

The vertical component of a vector of magnitude A making an angle θ with the positive X-axis is:

a. $A\cos\theta$ 

b. $A\sin\theta$ 

c. $A\tan\theta$ 

d. $A\cot\theta$ 

Correct Answer: b. $A\sin\theta$ 

Explanation:
The vertical (Y) component of a vector is given by:

$$A_y=A\sin\theta$$

---

MCQ No. 29

A vector makes an angle of 45° with the positive X-axis. Its X and Y components are:

a. Equal

b. X-component is greater

c. Y-component is greater

d. Both are zero

Correct Answer: a. Equal

Explanation:
Since

$$\cos45^\circ=\sin45^\circ,$$

both components are equal.

---

MCQ No. 30

The magnitude of a vector having components $A_x$ and $A_y$ is:

a. $A_x+A_y$

b. $A_x-A_y$

c. $\sqrt{A_x^2+A_y^2}$

d. $A_xA_y$

Correct Answer: c. $\sqrt{A_x^2+A_y^2}$

Explanation:
The magnitude of a vector is determined using the Pythagorean theorem.

---

MCQ No. 31

The direction of a vector with components $A_x$ and $A_y$ is determined by:

a. $\sin\theta=\dfrac{A_y}{A_x}$

b. $\cos\theta=\dfrac{A_y}{A_x}$

c. $\tan\theta=\dfrac{A_y}{A_x}$

d. $\tan\theta=\dfrac{A_x}{A_y}$

Correct Answer: c. $\tan\theta=\dfrac{A_y}{A_x}$

Explanation:
The direction of the resultant vector with respect to the X-axis is obtained using

$$\tan\theta=\frac{A_y}{A_x}.$$

---

MCQ No. 32

A vector of magnitude 10 N makes an angle of 30° with the positive X-axis. Its X-component is:

a. 5 N

b. 8.66 N

c. 10 N

d. 17.32 N

Correct Answer: b. 8.66 N

Explanation:

$$A_x=10\cos30^\circ=10\times0.866=8.66\,N$$

---

MCQ No. 33

A vector of magnitude 20 N makes an angle of 60° with the positive X-axis. Its Y-component is:

a. 10 N

b. 17.32 N

c. 20 N

d. 8.66 N

Correct Answer: b. 17.32 N

Explanation:

$$A_y=20\sin60^\circ=20\times0.866=17.32\,N$$

---

MCQ No. 34

A vector has components $3\hat{i}$  and $4\hat{j}$. Its magnitude is:

a. 3

b. 4

c. 5

d. 7

Correct Answer: c. 5

Explanation:

$$|A|=\sqrt{3^2+4^2}=5$$

---

MCQ No. 35

If the X-component of a vector is zero, the vector is directed along the:

a. X-axis

b. Y-axis

c. First quadrant

d. Fourth quadrant

Correct Answer: b. Y-axis

Explanation:
A zero X-component means the vector has only a vertical component.

---

MCQ No. 36

If the Y-component of a vector is zero, the vector is directed along the:

a. X-axis

b. Y-axis

c. Second quadrant

d. Third quadrant

Correct Answer: a. X-axis

Explanation:
A zero Y-component means the vector has only a horizontal component.

---

MCQ No. 37

The resultant of two vectors is obtained by:

a. Vector subtraction only

b. Vector multiplication

c. Vector addition

d. Scalar multiplication

Correct Answer: c. Vector addition

Explanation:
The combined effect of two or more vectors is called the resultant and is obtained by vector addition.

---

MCQ No. 38

Which graphical method is commonly used to add two vectors acting at the same point?

a. Polygon law

b. Triangle law

c. Parallelogram law

d. Right-hand rule

Correct Answer: c. Parallelogram law

Explanation:
The parallelogram law is used to determine the resultant of two vectors acting simultaneously at one point.

---

MCQ No. 39

The triangle law of vector addition is also known as the:

a. Head-to-tail rule

b. Right-hand rule

c. Left-hand rule

d. Polygon rule

Correct Answer: a. Head-to-tail rule

Explanation:
In the triangle law, the tail of one vector is placed at the head of the other.

---

MCQ No. 40

The polygon law is mainly used when:

a. Only one vector is present

b. Two vectors are added

c. More than two vectors are added

d. Multiplying vectors

Correct Answer: c. More than two vectors are added

Explanation:
The polygon law extends the triangle law for adding several vectors.

---

MCQ No. 41

The magnitude of the resultant of two equal vectors acting at 90° is:

a. A

b. 2A

c. $\sqrt{2}A$

d. Zero

Correct Answer: c. $\sqrt{2}A$

Explanation:

$$R=\sqrt{A^2+A^2}=\sqrt2A$$

---

MCQ No. 42

The magnitude of the resultant of two equal vectors becomes maximum when the angle between them is:

a. 0°

b. 45°

c. 90°

d. 180°

Correct Answer: a. 0°

Explanation:
When two vectors act in the same direction, their resultant is maximum.

---

MCQ No. 43

The magnitude of the resultant of two equal vectors becomes minimum when the angle between them is:

a. 0°

b. 60°

c. 90°

d. 180°

Correct Answer: d. 180°

Explanation:
Equal vectors acting in opposite directions cancel each other completely.

---

MCQ No. 44

Two equal vectors have zero resultant when the angle between them is:

a. 0°

b. 90°

c. 120°

d. 180°

Correct Answer: d. 180°

Explanation:
Vectors equal in magnitude and opposite in direction produce zero resultant.

---

MCQ No. 45

Two vectors of 3 N and 4 N act at right angles. Their resultant is:

a. 5 N

b. 7 N

c. 1 N

d. 12 N

Correct Answer: a. 5 N

Explanation:

$$R=\sqrt{3^2+4^2}=5\,N$$

---

MCQ No. 46

Two vectors of 6 N and 8 N act at right angles. Their resultant is:

a. 10 N

b. 12 N

c. 14 N

d. 16 N

Correct Answer: a. 10 N

Explanation:

$$R=\sqrt{6^2+8^2}=10\,N$$

---

MCQ No. 47

Two vectors of 5 N and 12 N act at right angles. Their resultant is:

a. 13 N

b. 17 N

c. 7 N

d. 10 N

Correct Answer: a. 13 N

Explanation:

$$R=\sqrt{5^2+12^2}=13\,N$$

---

MCQ No. 48

The angle made by a vector having components 3 and 4 with the positive X-axis is approximately:

a. 36.87°

b. 45°

c. 53.13°

d. 60°

Correct Answer: c. 53.13°

Explanation:

$$\tan\theta=\frac43$$

Therefore,

$$\theta=\tan^{-1}\left(\frac43\right)\approx53.13^\circ$$

---

MCQ No. 49

A vector of magnitude 10 N acts along the line $y=x$ . Each rectangular component is approximately:

a. 5 N

b. 7.07 N

c. 10 N

d. 14.14 N

Correct Answer: b. 7.07 N

Explanation:
Since the vector makes an angle of 45° with the X-axis,

$$A_x=A_y=10\cos45^\circ=\frac{10}{\sqrt2}\approx7.07\,N$$

---

MCQ No. 50

The resolution of vectors is particularly useful because it helps us:

a. Convert vectors into scalars

b. Simplify the addition and analysis of vectors

c. Eliminate vector quantities

d. Measure mass

Correct Answer: b. Simplify the addition and analysis of vectors

Explanation:
Resolving vectors into perpendicular components makes it easier to calculate resultants, analyze forces, and solve problems involving equilibrium and motion.

---

MCQs 51–75: Scalar Product (Dot Product) & Vector Product (Cross Product)

---

MCQ No. 51

The scalar product of two vectors $\vec{A}$ and $\vec{B}$ is given by:

a. $AB\sin \mathrm{\theta }$

b. $AB\cos\theta$ 

c. $A+B$ 

d. $A-\mathrm{B }$

Correct Answer: b. $AB\cos\theta$ 

Explanation: The scalar or dot product is defined as:

$$\vec{A}\cdot\vec{B}=AB\cos\theta$$

where $\theta$ is the angle between the two vectors.

---

MCQ No. 52

The scalar product of two vectors is a:

a. Vector quantity

b. Scalar quantity

c. Tensor quantity

d. Dimensionless quantity

Correct Answer: b. Scalar quantity

Explanation: The dot product results in a scalar quantity because it has magnitude only and no direction.

---

MCQ No. 53

The scalar product of two perpendicular vectors is:

a. Maximum

b. Zero

c. Minimum but not zero

d. Infinite

Correct Answer: b. Zero

Explanation: For perpendicular vectors, $\theta=90^\circ$  and $\cos90^\circ=0$ . Therefore:

$$\vec{A}\cdot\vec{B}=AB\cos90^\circ=0$$

---

MCQ No. 54

The scalar product of two parallel vectors is:

a. Zero

b. Maximum

c. Minimum

d. Undefined

Correct Answer: b. Maximum

Explanation: For parallel vectors, $\theta=0^\circ$  and $\cos0^\circ=1$ . Hence the dot product is maximum.

---

MCQ No. 55

If $\vec{A}\cdot\vec{B}=0$ , the vectors are:

a. Parallel

b. Perpendicular

c. Antiparallel

d. Equal

Correct Answer: b. Perpendicular

Explanation: A zero dot product indicates that the angle between the vectors is $90^\circ$, so they are perpendicular.

---

MCQ No. 56

The angle between two vectors can be determined using:

a. Cross product only

b. Dot product

c. Torque

d. Magnitude only

Correct Answer: b. Dot product

Explanation: The dot product formula is:

$$\cos\theta=\frac{\vec{A}\cdot\vec{B}}{AB}$$

which allows us to calculate the angle between two vectors.

---

MCQ No. 57

The scalar product of a vector with itself is equal to:

a. Its magnitude

b. Its magnitude squared

c. Zero

d. A unit vector

Correct Answer: b. Its magnitude squared

Explanation:

$$\vec{A}\cdot\vec{A}=A^2$$

because $\cos0^\circ=1$ .

---

MCQ No. 58

The vector product of two vectors $\vec{A}$ and $\vec{B}$ is given by:

a. $AB\cos\theta$ 

b. $AB\sin\theta$ 

c. $A+B$

d. $A-B$ 

Correct Answer: b. $AB\sin\theta$ 

Explanation: The magnitude of the cross product is:

$$|\vec{A}\times\vec{B}|=AB\sin\theta$$

---

MCQ No. 59

The vector product of two vectors is a:

a. Scalar quantity

b. Vector quantity

c. Dimensionless quantity

d. Constant quantity

Correct Answer: b. Vector quantity

Explanation: The cross product produces a vector quantity that has both magnitude and direction.

---

MCQ No. 60

The direction of the vector product $\vec{A}\times\vec{B}$ is determined by the:

a. Left-hand rule

b. Fleming’s left-hand rule

c. Right-hand rule

d. Polygon law

Correct Answer: c. Right-hand rule

Explanation: The right-hand rule determines the direction of the vector perpendicular to the plane containing $\vec{A}$ and $\vec{B}$ .

---

MCQ No. 61

The vector product of two parallel vectors is:

a. Maximum

b. Zero

c. Infinite

d. Undefined

Correct Answer: b. Zero

Explanation: For parallel vectors, $\theta=0^\circ$ and $\sin0^\circ=0$ . Therefore:

$$|\vec{A}\times\vec{B}|=0$$

---

MCQ No. 62

The vector product of two perpendicular vectors has magnitude:

a. Zero

b. $AB$ 

c. $A+\mathrm{B }$

d. $A-B$ 

Correct Answer: b. $AB$ 

Explanation: For perpendicular vectors, $\theta=90^\circ$  and $\sin90^\circ=1$ . Hence:

$$|\vec{A}\times\vec{B}|=AB$$

---

MCQ No. 63

The magnitude of the cross product is maximum when the angle between the vectors is:

a. $0^{\circ }$

b. $45^\circ$ 

c. $60^\circ$ 

d. $90^\circ$ 

Correct Answer: d. $90^\circ$ 

Explanation: The cross product depends on $\sin\theta$, which is maximum when $\theta=90^\circ$ .

---

MCQ No. 64

The direction of $\vec{A}\times\vec{B}$ is:

a. Parallel to $\vec{A}$ only

b. Parallel to $\vec{B}$ only

c. Perpendicular to both $\vec{A}$ and $\vec{B}$

d. Opposite to $\vec{A}$ only

Correct Answer: c. Perpendicular to both $\vec{A}$ and $\vec{B}$

Explanation: The cross product gives a vector perpendicular to the plane containing the two original vectors.

---

MCQ No. 65

If $\vec{A}\times\vec{B}=0$ , the vectors are:

a. Perpendicular

b. Parallel

c. At $45^\circ$ 

d. Equal in magnitude only

Correct Answer: b. Parallel

Explanation: A zero cross product means $\sin\theta=0$ , which occurs when the vectors are parallel or antiparallel.

---

MCQ No. 66

The scalar product is useful in determining the:

a. Direction of a vector

b. Area between vectors

c. Angle between vectors

d. Torque

Correct Answer: c. Angle between vectors

Explanation: The dot product formula contains $\cos\theta$, which is used to determine the angle between vectors.

---

MCQ No. 67

The vector product is useful in determining the:

a. Work done

b. Angle only

c. Area and perpendicular direction

d. Temperature

Correct Answer: c. Area and perpendicular direction

Explanation: The magnitude of the cross product represents the area of the parallelogram formed by the two vectors, and its direction is perpendicular to the plane.

---

MCQ No. 68

The projection of vector $\vec{A}$ on vector $\vec{B}$is:

a. $AB\sin\theta$

b. $AB\cos\theta$

c. $\frac{\vec{A}\cdot\vec{B}}{|\vec{B}|}$

d. $\vec{A}\times\vec{B}$

Correct Answer: c. $\frac{\vec{A}\cdot\vec{B}}{|\vec{B}|}$

Explanation: The projection of $\vec{A}$ on $\vec{B}$ is:

$$\frac{\vec{A}\cdot\vec{B}}{|\vec{B}|}$$

---

MCQ No. 69

For which angle is $|\vec{A}\cdot\vec{B}|=|\vec{A}\times\vec{B}|$?

a. $30^\circ$

b. $45^\circ$

c. ${60}^{\circ }$

d. $90^\circ$

Correct Answer: b. $45^\circ$

Explanation: The equality holds when:

$$AB\cos\theta=AB\sin\theta$$

which gives $\tan\theta=1$ and therefore $\theta=45^\circ$.

MCQ No. 70

The expression $\vec{A}\times\vec{B}=-(\vec{B}\times\vec{A})$ shows that the cross product is:

a. Commutative

b. Anticommutative

c. Associative

d. Distributive

Correct Answer: b. Anticommutative

Explanation: Reversing the order of vectors in a cross product reverses the direction of the resulting vector.

MCQ No. 71

The dot product of vectors $\hat{i}$  and $\hat{j}$is:

a. 1

b. 0

c. -1

d. $\hat{k}$

Correct Answer: b. 0

Explanation: Unit vectors $\hat{i}$ and $\hat{j}$ are perpendicular, so their dot product is zero.

---

MCQ No. 72

The cross product of vectors $\hat{i}$ and $\hat{j}$ is:

a. $\hat{i}$

b. $\hat{j}$

c. $\hat{k}$

d. 0

Correct Answer: c. $\stackrel{}{k}$

Explanation:

$$\hat{i}\times\hat{j}=\hat{k}$$

according to the right-hand rule.

---

MCQ No. 73

The cross product of vectors $\hat{j}$ and $\hat{k}$ is:

a. $\hat{i}$

b. $\hat{j}$

c. $\hat{k}$

d. 0

Correct Answer: a. $\widehat{i}$

Explanation:

$$\hat{j}\times\hat{k}=\hat{i}$$

---

MCQ No. 74

The cross product of vectors $\hat{k}$ and $\hat{i}$ is:

a. $\hat{i}$

b. $\hat{j}$

c. $\hat{k}$

d. 0

Correct Answer: b. $\hat{j}$

Explanation:

$$\hat{k}\times\hat{i}=\hat{j}$$

---

MCQ No. 75

The dot product of vectors $\hat{i}$ and $\hat{i}$ is:

a. 0

b. 1

c. -1

d. $\hat{i}$

Correct Answer: b. 1

Explanation: A unit vector dotted with itself gives:

$$\hat{i}\cdot\hat{i}=1$$

because the angle between them is $0^\circ$.

---

MCQs 76–100: Torque and Equilibrium

---

Torque is defined as the:

a. Scalar product of force and displacement

b. Vector product of position vector and force

c. Sum of force and displacement

d. Product of mass and acceleration

Correct Answer: b. Vector product of position vector and force

Explanation:
Torque is the turning effect of a force and is defined as the vector product of the position vector and the applied force:

$$\vec{\tau}=\vec{r}\times\vec{F}$$

---

MCQ No. 77

The SI unit of torque is:

a. Newton (N)

b. Joule (J)

c. Newton-metre (N·m)

d. Watt (W)

Correct Answer: c. Newton-metre (N·m)

Explanation:
The SI unit of torque is newton-metre (N·m). Although it has the same unit as work, torque is a vector quantity whereas work is a scalar quantity.

---

MCQ No. 78

Torque is a:

a. Scalar quantity

b. Vector quantity

c. Dimensionless quantity

d. Tensor quantity

Correct Answer: b. Vector quantity

Explanation:
Torque has both magnitude and direction. Its direction is determined by the right-hand rule.

---

MCQ No. 79

The magnitude of torque is given by:

a. $rF\cos\theta$

b. $rF\sin \theta$

c. $r+F$

d. $r-F$

Correct Answer: b. $rF\sin\theta$

Explanation:
The magnitude of torque depends on the applied force, the distance from the pivot, and the angle between them:

$$\tau=rF\sin\theta$$

---

MCQ No. 80

Torque is maximum when the angle between the position vector and force is:

a. $0^\circ$

b. $30^\circ$

c. $60^\circ$

d. $90^\circ$

Correct Answer: d. $90^\circ$

Explanation:
Since $\sin90^\circ=1$, the torque reaches its maximum value when the force acts perpendicular to the position vector.

---

MCQ No. 81

If the force acts along the position vector, the torque is:

a. Maximum

b. Zero

c. Half of its maximum value

d. Infinite

Correct Answer: b. Zero

Explanation:
When the force acts along the position vector, the angle is $0^\circ$. Therefore,

$$\tau=rF\sin0^\circ=0$$

---

MCQ No. 82

A force of 10 N acts perpendicular to a rod 2 m long. The torque produced is:

a. 5 N·m

b. 10 N·m

c. 20 N·m

d. 40 N·m

Correct Answer: c. 20 N·m

Explanation:

$$\tau=rF=2\times10=20\text{ N·m}$$

---

MCQ No. 83

A force of 5 N acts perpendicular to a rod 2 m long. The torque produced is:

a. 2.5 N·m

b. 5 N·m

c. 10 N·m

d. 20 N·m

Correct Answer: c. 10 N·m

Explanation:

$$\tau=rF=2\times5=10\text{ N·m}$$

---

MCQ No. 84

The perpendicular distance from the axis of rotation to the line of action of the force is called the:

a. Radius

b. Lever arm

c. Diameter

d. Height

Correct Answer: b. Lever arm

Explanation:
The lever arm (moment arm) is the perpendicular distance between the pivot and the line of action of the force.

---

MCQ No. 85

A longer spanner is preferred because it:

a. Reduces force

b. Increases torque

c. Reduces mass

d. Increases friction

Correct Answer: b. Increases torque

Explanation:
A longer spanner increases the lever arm, thereby increasing the torque for the same applied force.

---

MCQ No. 86

A door handle is fixed near the outer edge of the door because it:

a. Reduces the weight of the door

b. Increases the torque produced

c. Reduces friction at the hinge

d. Improves the appearance of the door

Correct Answer: b. Increases the torque produced

Explanation:
Placing the handle farther from the hinge increases the lever arm, making it easier to rotate the door.

---

MCQ No. 87

The first condition of equilibrium states that:

a. $\sum \tau =0$

b. $\sum F=0$

c. $\sum v=0$

d. $\sum a=0$

Correct Answer: b. $\sum F=0$

Explanation:
For translational equilibrium, the vector sum of all forces acting on the body must be zero.

---

MCQ No. 88

The first condition of equilibrium ensures:

a. Rotational equilibrium

b. Translational equilibrium

c. Circular motion

d. Uniform acceleration

Correct Answer: b. Translational equilibrium

Explanation:
When the resultant force is zero, the body has no linear acceleration.

---

MCQ No. 89

The second condition of equilibrium states that:

a. $\sum F=0$

b. $\sum\tau=0$

c. $\sum v=0$

d. $\sum a=0$

Correct Answer: b. $\sum\tau=0$

Explanation:
The algebraic sum of all clockwise and anticlockwise torques about any point must be zero.

---

MCQ No. 90

The second condition of equilibrium ensures:

a. Translational equilibrium

b. Rotational equilibrium

c. Uniform motion

d. Constant velocity

Correct Answer: b. Rotational equilibrium

Explanation:
A body remains free from angular acceleration when the net torque acting on it is zero.

---

MCQ No. 91

A body is said to be in complete equilibrium when:

a. Only the net force is zero.

b. Only the net torque is zero.

c. Both the net force and the net torque are zero.

d. Its velocity is always zero.

Correct Answer: c. Both the net force and the net torque are zero.

Explanation:
For complete equilibrium, both conditions must be satisfied simultaneously:

$$\sum F=0 \quad \text{and} \quad \sum\tau=0$$

---

MCQ No. 92

A body in translational equilibrium has:

a. Maximum acceleration

b. Zero resultant force

c. Maximum torque

d. Constant torque

Correct Answer: b. Zero resultant force

Explanation:
According to Newton's Second Law,

$$\sum F=ma$$

If $\sum F=0$, then the acceleration is zero.

---

MCQ No. 93

A body in rotational equilibrium has:

a. Zero resultant torque

b. Zero velocity

c. Infinite acceleration

d. Maximum force

Correct Answer: a. Zero resultant torque

Explanation:
A body is in rotational equilibrium when the algebraic sum of all torques acting on it is zero.

---

MCQ No. 94

If the resultant force acting on a body is zero, its acceleration is:

a. Maximum

b. Zero

c. Infinite

d. Constant but non-zero

Correct Answer: b. Zero

Explanation:
Newton's Second Law states:

$$F=ma$$

If the net force is zero, the acceleration must also be zero.

---

MCQ No. 95

A body in equilibrium may be:

a. Only at rest

b. Only moving uniformly

c. Either at rest or moving with constant velocity

d. Moving with constant acceleration

Correct Answer: c. Either at rest or moving with constant velocity

Explanation:
Equilibrium includes both static equilibrium (at rest) and dynamic equilibrium (moving with constant velocity).

---

MCQ No. 96

If a force acts through the pivot point, the torque produced is:

a. Maximum

b. Zero

c. Equal to the force

d. Infinite

Correct Answer: b. Zero

Explanation:
Since the lever arm is zero,

$$\tau=rF=0$$

---

MCQ No. 97

According to the usual sign convention, an anticlockwise torque is taken as:

a. Positive

b. Negative

c. Zero

d. Undefined

Correct Answer: a. Positive

Explanation:
By convention, anticlockwise torques are considered positive, while clockwise torques are considered negative.

---

MCQ No. 98

According to the usual sign convention, a clockwise torque is taken as:

a. Positive

b. Negative

c. Zero

d. Infinite

Correct Answer: b. Negative

Explanation:
Clockwise torques are assigned a negative sign when applying the second condition of equilibrium.

---

MCQ No. 99

In solving two-dimensional equilibrium problems, the first step is to:

a. Calculate torque only

b. Draw a free-body diagram showing all forces

c. Ignore the direction of forces

d. Calculate mass first

Correct Answer: b. Draw a free-body diagram showing all forces

Explanation:
A free-body diagram (FBD) helps identify all the forces and moments acting on the body before applying the conditions of equilibrium.

---

MCQ No. 100

Which pair of equations is used to solve two-dimensional equilibrium problems?

a. $\sum F=0$  and $\sum\tau=0$ 

b. $F=ma$ and $W=Fd$

c. $P=\frac{W}{t}$  and $V=\frac{d}{t}$

d. $KE=\frac12 mv^2$  and $PE=mgh$ 

Correct Answer: a. $\sum F=0$ and $\sum\tau=0$

Explanation:
Two-dimensional statics problems are solved by applying both conditions of equilibrium:

• First Condition: $\sum F=0$
  
• Second Condition: $\sum\tau=0$
  

---

📚 Continue Your Physics Preparation

If you found this quiz helpful, explore our complete collection of Physics learning resources.

🔬 Physics MCQs Hub

---

More Study Resources for Students and Teachers

• Computer Science 11th Class Notes (Main Page) 
• Computer Science 12th Class Notes (Main Page) 

************************************

1. English Poems Analysis Hub– A to Z Index (English Poetry) 

(https://poemanalysishub.blogspot.com/p/english-poems-analysis-to-z-index.html)

2. Website for School and College Level Mathematics  

(https://askraremaths.blogspot.com)

3. ASK Rare Class Notes – Study Resources for Students & Teachers 

(https://askrareclassnotes.blogspot.com/)

© 2026 & onwards Academic Skills and Knowledge (ASK)   

Note:  Write me in the comments box below for any query and also Share this information with your classmates and friends.

---

© https://askrareclassnotes.blogspot.com | Learn • Practice • Succeed

---

Best Tools and Supplies for Students and Teachers:

📚 Grammar Books – Improve Writing, Score Higher
🪑 Study Chairs – Sit Comfortably, Study Better
🛋️ Study Desks – Organized Space, Better Learning
💡 Desk Lamps – Bright Light, Better Focus
⌚ Digital Watches– Manage Time, Improve Results
📱 Phone Stands – Hands-Free Learning Made Easy
🎧 Headphones – Focus Better, Learn Without Distractions
⌨️ Wireless Keyboards – Type Faster, Work Smarter
🖱️ Wireless Mouse – Smooth Control, Better Workflow
🖨️ Printers – Print Smart, Save Time

Disclosure: The above links on this page are affiliate links. This means that if you make a purchase through them, I may earn a small commission at no additional cost to you. Your support helps me maintain, improve, and continue providing valuable free content on this website.

With Best Regards

ASKRare Team

---

---