Vectors and Equilibrium – 100 Advanced & Numerical MCQs with Solutions | ECAT, MDCAT & Engineering Entry Tests

100 Advanced & Numerical MCQs (Level -2) 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-II – 100 Advanced & Numerical MCQs (101–200) on Vectors and Equilibrium

---

MCQs 101–125: Vector Resolution and Resultant of Vectors

---

MCQ No. 101

A vector of magnitude 20 N makes an angle of 30° with the positive X-axis. Its horizontal component is:

a. 10 N

b. 17.32 N

c. 20 N

d. 5 N

Correct Answer: b. 17.32 N

Explanation:

$$R_x=R\cos\theta=20\cos30^\circ=20(0.866)=17.32\,N$$

---

MCQ No. 102

A force of 40 N acts at an angle of 60° with the positive X-axis. Its vertical component is:

a. 20 N

b. 34.64 N

c. 40 N

d. 10 N

Correct Answer: b. 34.64 N

Explanation:

$$R_y=R\sin60^\circ=40(0.866)=34.64\,N$$

---

MCQ No. 103

A vector has components 8 N along the X-axis and 6 N along the Y-axis. Its magnitude is:

a. 10 N

b. 12 N

c. 14 N

d. 2 N

Correct Answer: a. 10 N

Explanation:

$$R=\sqrt{8^2+6^2} =\sqrt{64+36} =\sqrt{100}=10\,N$$

---

MCQ No. 104

A vector has components 12 N and 5 N. Its magnitude is:

a. 13 N

b. 15 N

c. 17 N

d. 7 N

Correct Answer: a. 13 N

Explanation:

$$R=\sqrt{12^2+5^2} =\sqrt{169} =13\,N$$

---

MCQ No. 105

The direction of a vector having components 8 N and 6 N is approximately:

a. 30°

b. 36.87°

c. 45°

d. 60°

Correct Answer: b. 36.87°

Explanation:

$$\tan\theta=\frac{6}{8}=0.75$$
$$\theta=\tan^{-1}(0.75)\approx36.87^\circ$$

---

MCQ No. 106

A vector of magnitude 50 N acts at 53° with the X-axis. Its horizontal component is approximately:

a. 30 N

b. 40 N

c. 50 N

d. 25 N

Correct Answer: a. 30 N

Explanation:

$$R_x=50\cos53^\circ \approx50(0.6)=30\,N$$

---

MCQ No. 107

The vertical component of the vector in MCQ 106 is approximately:

a. 30 N

b. 40 N

c. 50 N

d. 25 N

Correct Answer: b. 40 N

Explanation:

$$R_y=50\sin53^\circ \approx50(0.8)=40\,N$$

---

MCQ No. 108

Two perpendicular forces of 5 N and 12 N act on a particle. Their resultant is:

a. 13 N

b. 17 N

c. 7 N

d. 10 N

Correct Answer: a. 13 N

Explanation:

$$R=\sqrt{5^2+12^2} =\sqrt{169} =13\,N$$

---

MCQ No. 109

Two perpendicular forces of 8 N and 15 N produce a resultant of:

a. 17 N

b. 20 N

c. 23 N

d. 7 N

Correct Answer: a. 17 N

Explanation:

$$R=\sqrt{8^2+15^2} =\sqrt{289} =17\,N$$

---

MCQ No. 110

Two forces of 9 N and 12 N act at right angles. Their resultant is:

a. 15 N

b. 18 N

c. 21 N

d. 3 N

Correct Answer: a. 15 N

Explanation:

$$R=\sqrt{9^2+12^2} =\sqrt{225} =15\,N$$

---

MCQ No. 111

Two equal forces each of 20 N act in the same direction. Their resultant is:

a. 20 N

b. 40 N

c. 0 N

d. 28.3 N

Correct Answer: b. 40 N

Explanation:
When forces act in the same direction, their magnitudes are added directly.

---

MCQ No. 112

Two equal forces each of 20 N act in opposite directions. Their resultant is:

a. 40 N

b. 20 N

c. 0 N

d. 10 N

Correct Answer: c. 0 N

Explanation:
Equal forces acting in opposite directions cancel each other.

---

MCQ No. 113

Two forces of 10 N each act at 90°. Their resultant is:

a. 10 N

b. 14.14 N

c. 20 N

d. 0 N

Correct Answer: b. 14.14 N

Explanation:

$$R=\sqrt{10^2+10^2} =10\sqrt2 \approx14.14\,N$$

---

MCQ No. 114

Two forces of 10 N each act at 180°. Their resultant is:

a. 20 N

b. 14.14 N

c. 10 N

d. 0 N

Correct Answer: d. 0 N

Explanation:
Equal forces acting in opposite directions produce zero resultant.

---

MCQ No. 115

The resultant of two vectors is always:

a. Smaller than each vector

b. Greater than each vector

c. Between the difference and the sum of their magnitudes

d. Equal to one of the vectors

Correct Answer: c. Between the difference and the sum of their magnitudes

Explanation:
The magnitude of the resultant satisfies:

$$|A-B|\le R\le A+B$$

---

MCQ No. 116

The angle between two vectors is 0°. Their resultant magnitude is:

a. $A+B$ 

b. $A-B$ 

c. $\sqrt{A^2+B^2}$

d. Zero

Correct Answer: a. $A+B$ 

Explanation:
When vectors act in the same direction, their magnitudes simply add.

---

MCQ No. 117

The angle between two vectors is 180°. Their resultant magnitude is:

a. $A+B$ 

b. $|A-B|$ 

c. $\sqrt{A^2+B^2}$

d. Zero always

Correct Answer: b. $|A-B|$ 

Explanation:
For opposite directions, the resultant equals the difference in magnitudes.

---

MCQ No. 118

Two vectors each of 30 N act at right angles. Their resultant is:

a. 30 N

b. 42.4 N

c. 60 N

d. 90 N

Correct Answer: b. 42.4 N

Explanation:

$$R=30\sqrt2 \approx42.4\,N$$

---

MCQ No. 119

If the horizontal component of a vector is 24 N and its vertical component is 7 N, its magnitude is:

a. 25 N

b. 26 N

c. 27 N

d. 31 N

Correct Answer: a. 25 N

Explanation:

$$R=\sqrt{24^2+7^2} =\sqrt{625} =25\,N$$

---

MCQ No. 120

A vector makes an angle whose tangent is 3/4. The angle is approximately:

a. 30°

b. 36.87°

c. 45°

d. 53.13°

Correct Answer: b. 36.87°

Explanation:

$$\theta=\tan^{-1}\left(\frac34\right)\approx36.87^\circ$$

---

MCQ No. 121

The horizontal component of a vector is always obtained using:

a. Sine function

b. Cosine function

c. Tangent function

d. Cotangent function

Correct Answer: b. Cosine function

Explanation:

$$R_x=R\cos\theta$$

---

MCQ No. 122

The vertical component of a vector is always obtained using:

a. Cosine function

b. Tangent function

c. Sine function

d. Cotangent function

Correct Answer: c. Sine function

Explanation:

$$R_y=R\sin\theta$$

---

MCQ No. 123

The resultant of perpendicular vectors is calculated using:

a. Addition rule

b. Subtraction rule

c. Pythagoras' theorem

d. Division rule

Correct Answer: c. Pythagoras' theorem

Explanation:
Perpendicular components form a right triangle; therefore, the resultant is found using the Pythagorean theorem.

---

MCQ No. 124

The direction of a resultant vector obtained from rectangular components is determined using:

a. $\sin\theta$ 

b. $\cos\theta$ 

c. $\tan\theta=\dfrac{R_y}{R_x}$

d. $\cot\theta$ 

Correct Answer: c. $\tan\theta=\dfrac{R_y}{R_x}$

Explanation:
The direction is calculated using the tangent ratio of the vertical and horizontal components.

---

MCQ No. 125

Resolving forces into rectangular components is mainly useful for:

a. Measuring temperature

b. Solving equilibrium and motion problems

c. Calculating density

d. Finding pressure only

Correct Answer: b. Solving equilibrium and motion problems

Explanation:
Vector resolution simplifies the analysis of forces acting in different directions and is essential for solving problems in mechanics and equilibrium.

---

MCQs 126–150: Scalar Product (Dot Product), Vector Product (Cross Product) & Applications

---

MCQ No. 126

Two vectors of magnitudes 6 and 8 make an angle of 60°. Their scalar product is:

a. 24

b. 48

c. 36

d. 12

Correct Answer: a. 24

Explanation:

$$\vec A \cdot \vec B = AB\cos\theta$$
$$=6\times8\times\cos60^\circ$$
$$=48\times\frac12=24$$

---

MCQ No. 127

Two vectors of magnitudes 10 and 5 are perpendicular. Their scalar product is:

a. 50

b. 25

c. 0

d. 15

Correct Answer: c. 0

Explanation:

Since

$$\cos90^\circ=0,$$
$$\vec A\cdot\vec B=0$$

---

MCQ No. 128

Two vectors each having magnitude 8 are parallel. Their scalar product is:

a. 0

b. 32

c. 64

d. 128

Correct Answer: c. 64

Explanation:

$$8\times8\times\cos0^\circ=64$$

---

MCQ No. 129

Two vectors each having magnitude 12 act in opposite directions. Their scalar product is:

a. 144

b. -144

c. 0

d. 72

Correct Answer: b. -144

Explanation:

$$\cos180^\circ=-1$$

Therefore,

$$12\times12\times(-1)=-144$$

---

MCQ No. 130

If

$$\vec A\cdot\vec B=50,\quad |\vec A|=10,\quad |\vec B|=10$$

the angle between them is:

a. 30°

b. 45°

c. 60°

d. 90°

Correct Answer: c. 60°

Explanation:

$$\vec{A}\cdot \vec{B}=AB\cos \theta \mathrm{<br>}$$

$$50=10\times10\cos\theta$$
$$\cos\theta=\frac12$$

Hence,

$$\theta=60^\circ$$

---

MCQ No. 131

Two vectors of magnitudes 5 and 12 are perpendicular. Their vector product is:

a. 17

b. 60

c. 0

d. 25

Correct Answer: b. 60

Explanation:

$$|\vec A\times\vec B| =AB\sin90^\circ =5\times12 =60$$

---

MCQ No. 132

Two vectors each of magnitude 10 are parallel. Their vector product is:

a. 100

b. 50

c. 0

d. 10

Correct Answer: c. 0

Explanation:

Since

$$\sin0^\circ=0,$$

the cross product is zero.

---

MCQ No. 133

Two vectors each of magnitude 15 make an angle of 30°. Their vector product is:

a. 112.5

b. 225

c. 195

d. 75

Correct Answer: a. 112.5

Explanation:

$$15\times15\times\sin30^\circ$$
$$225\times\frac12 =112.5$$

---

MCQ No. 134

If

$$|\vec A|=6,\quad |\vec B|=8,\quad |\vec A\times\vec B|=48$$

then the angle between the vectors is:

a. 30°

b. 45°

c. 60°

d. 90°

Correct Answer: d. 90°

Explanation:

$$48=6\times8\times\sin\theta$$
$$48=48\sin\theta$$

Hence,

$$\sin\theta=1$$

Therefore,

$$\theta=90^\circ$$

---

MCQ No. 135

The angle between two vectors is 45°. If each vector has magnitude 10, then their scalar product is:

a. 50

b. 70.7

c. 100

d. 141.4

Correct Answer: b. 70.7

Explanation:

$$10\times10\times\cos45^\circ$$
$$100\times0.707 =70.7$$

---

MCQ No. 136

For the vectors in MCQ 135, the magnitude of their vector product is:

a. 50

b. 70.7

c. 100

d. 141.4

Correct Answer: b. 70.7

Explanation:

$$10\times10\times\sin45^\circ =70.7$$

---

MCQ No. 137

A force of 50 N acts in the same direction as a displacement of 4 m. The work done is:

a. 50 J

b. 100 J

c. 200 J

d. Zero

Correct Answer: c. 200 J

Explanation:

$$W=Fs\cos\theta$$
$$=50\times4\times\cos0^\circ =200J$$

---

MCQ No. 138

A force of 20 N acts perpendicular to a displacement of 5 m. The work done is:

a. 100 J

b. 50 J

c. 20 J

d. 0 J

Correct Answer: d. 0 J

Explanation:

Since

$$\cos90^\circ=0,$$

no work is done.

---

MCQ No. 139

The work done by a force is maximum when the angle between force and displacement is:

a. 0°

b. 45°

c. 90°

d. 180°

Correct Answer: a. 0°

Explanation:

Work depends on

$$W=Fs\cos\theta$$

and is maximum when

$$\cos0^\circ=1.$$

---

MCQ No. 140

The work done becomes negative when the angle between force and displacement is:

a. 0°

b. 60°

c. 90°

d. 180°

Correct Answer: d. 180°

Explanation:

Since

$$\cos180^\circ=-1,$$

the work done is negative.

---

MCQ No. 141

A force of 30 N acts perpendicular to a rod 0.5 m long. The torque produced is:

a. 10 N·m

b. 15 N·m

c. 20 N·m

d. 30 N·m

Correct Answer: b. 15 N·m

Explanation:

$$\tau=rF$$
$$=0.5\times30 =15\text{ N·m}$$

---

MCQ No. 142

A force of 40 N acts at 90° on a 0.25 m wrench. The torque is:

a. 5 N·m

b. 10 N·m

c. 15 N·m

d. 20 N·m

Correct Answer: b. 10 N·m

Explanation:

$$\tau=rF =0.25\times40 =10\text{ N·m}$$

---

MCQ No. 143

A force of 25 N acts along a rod of length 2 m. The torque produced is:

a. 50 N·m

b. 25 N·m

c. Zero

d. 2 N·m

Correct Answer: c. Zero

Explanation:

Since the force acts along the rod,

$$\theta=0^\circ$$

Hence,

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

---

MCQ No. 144

The direction of torque is determined by:

a. Fleming's Left-Hand Rule

b. Fleming's Right-Hand Rule

c. Right-Hand Thumb Rule

d. Lenz's Law

Correct Answer: c. Right-Hand Thumb Rule

Explanation:
The direction of the torque vector is obtained using the Right-Hand Thumb Rule.

---

MCQ No. 145

A mechanic uses a longer wrench mainly to:

a. Reduce force

b. Reduce friction

c. Increase torque

d. Increase mass

Correct Answer: c. Increase torque

Explanation:
Increasing the lever arm increases the torque for the same applied force.

---

MCQ No. 146

Which physical quantity is calculated using the scalar product?

a. Torque

b. Angular momentum

c. Work

d. Moment of inertia

Correct Answer: c. Work

Explanation:
Work is given by

$$W=\vec F\cdot\vec s$$

---

MCQ No. 147

Which physical quantity is calculated using the vector product?

a. Work

b. Power

c. Torque

d. Pressure

Correct Answer: c. Torque

Explanation:

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

---

MCQ No. 148

If two non-zero vectors have both zero dot product and zero cross product simultaneously, then the vectors are:

a. Parallel

b. Perpendicular

c. Impossible

d. Equal

Correct Answer: c. Impossible

Explanation:
For non-zero vectors:

• Dot product = 0 ⇒ vectors are perpendicular.
• Cross product = 0 ⇒ vectors are parallel.

A pair of non-zero vectors cannot be both perpendicular and parallel simultaneously.

---

MCQ No. 149

The projection of a vector on a perpendicular direction is:

a. Maximum

b. Equal to its magnitude

c. Zero

d. Negative

Correct Answer: c. Zero

Explanation:
The projection depends on

$$A\cos\theta.$$

For

$$\theta=90^\circ,$$

the projection becomes zero.

---

MCQ No. 150

A student wants to maximize the turning effect of a force applied to a wrench. The force should be applied:

a. Parallel to the wrench

b. At an angle of 30°

c. At an angle of 45°

d. Perpendicular to the wrench

Correct Answer: d. Perpendicular to the wrench

Explanation:
The turning effect (torque) is maximum when the force acts perpendicular to the lever arm because

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

and

$$\sin90^\circ=1.$$

---

MCQs 151–175: Advanced Equilibrium & Two-Dimensional Statics

---

MCQ No. 151

A body is in translational equilibrium when:

a. Net torque is zero

b. Net force is zero

c. Velocity is zero

d. Acceleration is maximum

Correct Answer: b. Net force is zero

Explanation:

According to the first condition of equilibrium,

$$\sum \vec{F}=0$$

This means the resultant force acting on the body must be zero.

---

MCQ No. 152

A body is in rotational equilibrium when:

a. Net force is maximum

b. Net torque is zero

c. Velocity is constant

d. Mass is zero

Correct Answer: b. Net torque is zero

Explanation:

The second condition of equilibrium states:

$$\sum \tau=0$$

Hence, clockwise and anticlockwise torques balance each other.

---

MCQ No. 153

A body remains in complete equilibrium when:

a. Only the first condition is satisfied

b. Only the second condition is satisfied

c. Both conditions are satisfied simultaneously

d. The body is at rest only

Correct Answer: c. Both conditions are satisfied simultaneously

Explanation:

For complete equilibrium,

$$\sum \vec F=0$$

and

$$\sum \tau=0$$

must both be satisfied.

---

MCQ No. 154

A force of 20 N acts at a perpendicular distance of 0.5 m from the pivot. The torque is:

a. 5 N·m

b. 10 N·m

c. 15 N·m

d. 20 N·m

Correct Answer: b. 10 N·m

Explanation:

$$\tau=Fr$$
$$=20\times0.5=10\text{ N·m}$$

---

MCQ No. 155

A force of 40 N acts 0.25 m from the pivot at 90°. The torque produced is:

a. 5 N·m

b. 8 N·m

c. 10 N·m

d. 20 N·m

Correct Answer: c. 10 N·m

Explanation:

$$\tau=Fr$$
$$=40\times0.25=10\text{ N·m}$$

---

MCQ No. 156

A 15 N force acts 2 m from the pivot and is perpendicular to the rod. The torque is:

a. 20 N·m

b. 25 N·m

c. 30 N·m

d. 35 N·m

Correct Answer: c. 30 N·m

Explanation:

$$\tau=Fr$$
$$=15\times2=30\text{ N·m}$$

---

MCQ No. 157

A force acts through the pivot point of a lever. The torque produced is:

a. Maximum

b. Equal to the force

c. Zero

d. Infinite

Correct Answer: c. Zero

Explanation:

Since the perpendicular distance is zero,

$$\tau=Fr=0$$

---

MCQ No. 158

A 50 N force acts 0.8 m from the pivot. What is the torque if the force is perpendicular?

a. 20 N·m

b. 30 N·m

c. 40 N·m

d. 50 N·m

Correct Answer: c. 40 N·m

Explanation:

$$\tau=50\times0.8=40\text{ N·m}$$

---

MCQ No. 159

A beam is balanced by 30 N·m clockwise torque. The required anticlockwise torque is:

a. 15 N·m

b. 20 N·m

c. 25 N·m

d. 30 N·m

Correct Answer: d. 30 N·m

Explanation:

For rotational equilibrium,

$$\text{Clockwise torque}=\text{Anticlockwise torque}$$

---

MCQ No. 160

A 10 N force acts 3 m from the pivot. The torque is:

a. 20 N·m

b. 25 N·m

c. 30 N·m

d. 35 N·m

Correct Answer: c. 30 N·m

Explanation:

$$\tau =10\times 3=30\text{ N.m}\text{<span style="color: \#cc0000;"><br></span>}$$

---

MCQ No. 161

A beam is in equilibrium under two opposite forces of 25 N each. The resultant force is:

a. 50 N

b. 25 N

c. 0 N

d. Depends on distance

Correct Answer: c. 0 N

Explanation:

Equal and opposite forces cancel each other.

---

MCQ No. 162

A beam experiences 60 N·m clockwise torque and 45 N·m anticlockwise torque. The net torque is:

a. 15 N·m clockwise

b. 15 N·m anticlockwise

c. 105 N·m

d. Zero

Correct Answer: a. 15 N·m clockwise

Explanation:

$$60-45=15\text{ N·m}$$

The larger torque determines the direction.

---

MCQ No. 163

A force of 12 N acts 0.5 m from the pivot. The torque produced is:

a. 4 N·m

b. 5 N·m

c. 6 N·m

d. 8 N·m

Correct Answer: c. 6 N·m

Explanation:

$$12\times0.5=6\text{ N·m}$$

---

MCQ No. 164

A 6 N force is applied 4 m from the pivot. The torque is:

a. 18 N·m

b. 20 N·m

c. 24 N·m

d. 30 N·m

Correct Answer: c. 24 N·m

Explanation:

$$6\times4=24\text{ N·m}$$

---

MCQ No. 165

If the applied force is doubled while the lever arm remains constant, the torque becomes:

a. Half

b. Double

c. Four times

d. Unchanged

Correct Answer: b. Double

Explanation:

Since

$$\tau=Fr,$$

doubling the force doubles the torque.

---

MCQ No. 166

If the lever arm is doubled while the force remains constant, the torque becomes:

a. Half

b. Double

c. Four times

d. Zero

Correct Answer: b. Double

Explanation:

Torque is directly proportional to the lever arm.

---

MCQ No. 167

Which of the following tools works mainly on the principle of torque?

a. Thermometer

b. Screwdriver

c. Spanner

d. Ammeter

Correct Answer: c. Spanner

Explanation:

A spanner increases the turning effect (torque) to loosen or tighten nuts and bolts.

---

MCQ No. 168

Which quantity should be drawn first while solving an equilibrium problem?

a. Velocity diagram

b. Free-body diagram

c. Circuit diagram

d. Ray diagram

Correct Answer: b. Free-body diagram

Explanation:

A free-body diagram clearly shows all the forces acting on the body.

---

MCQ No. 169

In a free-body diagram, all forces are represented by:

a. Scalars

b. Arrows

c. Circles

d. Numbers only

Correct Answer: b. Arrows

Explanation:

Arrows indicate both the magnitude and direction of each force.

---

MCQ No. 170

The SI unit of the moment of force is:

a. Joule

b. Newton

c. Newton-metre

d. Watt

Correct Answer: c. Newton-metre

Explanation:

Torque or moment of force is measured in N·m.

---

MCQ No. 171

A seesaw remains horizontal because:

a. Both children have equal masses only

b. Clockwise and anticlockwise torques are balanced

c. Gravity is absent

d. Friction is zero

Correct Answer: b. Clockwise and anticlockwise torques are balanced

Explanation:

A balanced seesaw satisfies the second condition of equilibrium.

---

MCQ No. 172

The first condition of equilibrium is based on:

a. Newton's First Law of Motion

b. Newton's Second Law of Motion

c. Newton's Third Law of Motion

d. Law of Gravitation

Correct Answer: b. Newton's Second Law of Motion

Explanation:

From

$$\sum F=ma,$$

if the net force is zero, acceleration is zero.

---

MCQ No. 173

If the clockwise torque is greater than the anticlockwise torque, the body will:

a. Rotate clockwise

b. Rotate anticlockwise

c. Remain stationary

d. Move upward

Correct Answer: a. Rotate clockwise

Explanation:

The body rotates in the direction of the greater net torque.

---

MCQ No. 174

The condition

$$\sum F_x=0$$

indicates that:

a. Horizontal forces are balanced

b. Vertical forces are balanced

c. Torque is zero

d. Work done is zero

Correct Answer: a. Horizontal forces are balanced

Explanation:

For equilibrium in two dimensions, the algebraic sum of all horizontal forces must be zero.

---

MCQ No. 175

For a body in two-dimensional equilibrium, which set of equations must be satisfied?

a. $\sum F_x=0,\; \sum F_y=0,\; \sum \tau=0$ 

b. $F=ma,W=F\mathrm{s }$

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

d. $KE=\frac12 mv^2,\; PE=mgh$ 

Correct Answer: a. $\sum F_x=0,\; \sum F_y=0,\; \sum \tau=0$ 

Explanation:

To solve two-dimensional statics problems, all three equilibrium equations must be satisfied:

• Horizontal forces balance: $\sum F_x=0$ 
• Vertical forces balance: $\sum F_y=\mathrm{0 }$
• Clockwise and anticlockwise torques balance: $\sum \tau =\mathrm{0 }$

---

MCQs 176–200: Mixed Numerical Problems on Vectors, Torque & Equilibrium

---

MCQ No. 176

A force of 60 N acts perpendicular to a rod of length 0.5 m. The torque produced is:

a. 15 N·m

b. 20 N·m

c. 30 N·m

d. 60 N·m

Correct Answer: c. 30 N·m

Explanation:

$$\tau = Fr$$
$$=60\times0.5=30\text{ N·m}$$

---

MCQ No. 177

A 25 N force acts 0.8 m from the pivot at 90°. The torque is:

a. 10 N·m

b. 15 N·m

c. 20 N·m

d. 25 N·m

Correct Answer: c. 20 N·m

Explanation:

$$\tau=25\times0.8=20\text{ N·m}$$

---

MCQ No. 178

A vector has components 9 N along the X-axis and 12 N along the Y-axis. Its magnitude is:

a. 13 N

b. 15 N

c. 18 N

d. 21 N

Correct Answer: b. 15 N

Explanation:

$$R=\sqrt{9^2+12^2} =\sqrt{225} =15\text{ N}$$

---

MCQ No. 179

The direction of the vector in MCQ 178 is approximately:

a. 36.87°

b. 45°

c. 53.13°

d. 60°

Correct Answer: c. 53.13°

Explanation:

$$\tan\theta=\frac{12}{9} =\frac43$$
$$\theta\approx53.13^\circ$$

---

MCQ No. 180

Two vectors of 20 N each act at right angles. Their resultant is:

a. 20 N

b. 28.3 N

c. 40 N

d. 56.6 N

Correct Answer: b. 28.3 N

Explanation:

$$R=20\sqrt2 \approx28.3\text{ N}$$

---

MCQ No. 181

Two vectors of 15 N each act in opposite directions. Their resultant is:

a. 30 N

b. 15 N

c. 0 N

d. 7.5 N

Correct Answer: c. 0 N

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

---

MCQ No. 182

Two vectors each having magnitude 10 make an angle of 60°. Their scalar product is:

a. 25

b. 50

c. 75

d. 100

Correct Answer: b. 50

Explanation:

$$10\times10\times\cos60^\circ =100\times0.5 =50$$

---

MCQ No. 183

Two vectors each having magnitude 10 are perpendicular. Their vector product is:

a. 0

b. 50

c. 100

d. 200

Correct Answer: c. 100

Explanation:

$$10\times10\times\sin90^\circ =100$$

---

MCQ No. 184

A force of 80 N moves an object through 5 m in the same direction. The work done is:

a. 200 J

b. 300 J

c. 400 J

d. 500 J

Correct Answer: c. 400 J

Explanation:

$$W=Fs =80\times5 =400\text{ J}$$

---

MCQ No. 185

A 40 N force acts perpendicular to a displacement of 8 m. The work done is:

a. 320 J

b. 160 J

c. 40 J

d. 0 J

Correct Answer: d. 0 J

Explanation:

Since

$$\cos90^\circ=0,$$

the work done is zero.

---

MCQ No. 186

A force of 18 N acts perpendicular to a 2 m rod. The torque produced is:

a. 18 N·m

b. 20 N·m

c. 36 N·m

d. 40 N·m

Correct Answer: c. 36 N·m

Explanation:

$$\tau=18\times2=36\text{ N·m}$$

---

MCQ No. 187

If the applied force is tripled while the lever arm remains unchanged, the torque becomes:

a. Unchanged

b. Double

c. Triple

d. Four times

Correct Answer: c. Triple

Explanation:

Since

$$\tau=Fr,$$

tripling the force triples the torque.

---

MCQ No. 188

A 10 N force acts 4 m from the pivot. The torque is:

a. 20 N·m

b. 30 N·m

c. 40 N·m

d. 50 N·m

Correct Answer: c. 40 N·m

Explanation:

$$10\times4=40\text{ N·m}$$

---

MCQ No. 189

The angle between two vectors is 90°. Their:

a. Dot product is maximum.

b. Cross product is zero.

c. Dot product is zero.

d. Both products are zero.

Correct Answer: c. Dot product is zero.

Explanation:

For perpendicular vectors,

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

---

MCQ No. 190

The angle between two vectors is 0°. Their cross product is:

a. Maximum

b. Minimum but not zero

c. Zero

d. Equal to their sum

Correct Answer: c. Zero

Explanation:

Since

$$\sin0^\circ=0,$$

their vector product is zero.

---

MCQ No. 191

A body is in equilibrium when:

a. Only the resultant force is zero.

b. Only the resultant torque is zero.

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

d. Its speed is always zero.

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

Explanation:

Complete equilibrium requires:

$$\sum F=0$$

and

$$\sum\tau=0.$$

---

MCQ No. 192

For a body in two-dimensional equilibrium,

$$\sum F_x=$$

a. 1

b. Force

c. 0

d. Torque

Correct Answer: c. 0

Explanation:

Horizontal forces must balance each other.

---

MCQ No. 193

For a body in two-dimensional equilibrium,

$$\sum F_y=$$

a. 0

b. 1

c. mg

d. Torque

Correct Answer: a. 0

Explanation:

The algebraic sum of vertical forces must also be zero.

---

MCQ No. 194

For rotational equilibrium,

$$\sum\tau=$$

a. 1

b. mg

c. F

d. 0

Correct Answer: d. 0

Explanation:

Clockwise and anticlockwise moments must balance.

---

MCQ No. 195

Which quantity is obtained from the vector product of the position vector and force?

a. Work

b. Momentum

c. Torque

d. Power

Correct Answer: c. Torque

Explanation:

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

---

MCQ No. 196

The turning effect of a force is called:

a. Work

b. Energy

c. Torque

d. Momentum

Correct Answer: c. Torque

Explanation:
Torque is the rotational effect produced by a force acting at some distance from the axis of rotation.

---

MCQ No. 197

A longer handle on a wrench makes it easier to rotate a nut because it:

a. Increases the applied force

b. Reduces the weight

c. Increases the lever arm

d. Decreases friction

Correct Answer: c. Increases the lever arm

Explanation:
A larger lever arm increases the torque produced for the same force.

---

MCQ No. 198

The vector product of two vectors is maximum when the angle between them is:

a. 0°

b. 30°

c. 60°

d. 90°

Correct Answer: d. 90°

Explanation:

Since

$$|\vec A\times\vec B|=AB\sin\theta,$$

its maximum value occurs when

$$\sin90^\circ=1.$$

---

MCQ No. 199

The scalar product of two vectors is maximum when the angle between them is:

a. 0°

b. 45°

c. 90°

d. 180°

Correct Answer: a. 0°

Explanation:

Since

$$\vec A\cdot\vec B=AB\cos\theta,$$

the maximum value occurs when

$$\cos0^\circ=1.$$

---

MCQ No. 200

Which of the following best summarizes the requirements for solving two-dimensional equilibrium problems?

a. Apply only Newton's Second Law.

b. Apply only the first condition of equilibrium.

c. Apply only the second condition of equilibrium.

d. Apply the equations $\sum F_x=0$ , $\sum F_y=0$ , and $\sum\tau=0$ .

Correct Answer: d. Apply the equations $\sum F_x=0$ , $\sum F_y=0$ , and $\sum\tau=0$ .

Explanation:
A body in two-dimensional equilibrium must satisfy all three equations simultaneously:

• $\sum F_x=0$ 
• $\sum F_y=\mathrm{0 }$
• $\sum\tau=0$ 

---

📚 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

---

---