Statics: Master the Fundamentals of Equilibrium and Forces

Question 1

For a rigid body to be in equilibrium, which condition is NOT required?

Accepted Answer

Body is stationary

Answer

Zero net force acting on the body

Answer

Zero net moment acting on the body

Answer

Balanced forces acting on the body

Question 2

For a rigid body in equilibrium under the influence of three forces F1, F2, and F3, which statement accurately describes the equilibrium conditions?

Accepted Answer

The vector sum of F1, F2, and F3 is zero, and the sum of their moments about any point is also zero.

Answer

The forces F1 and F2 act along the same line, while F3 acts perpendicular to their resultant.

Answer

The forces F1 and F3 have equal magnitudes but opposite directions, while F2 acts at a right angle to both F1 and F3.

Answer

The lines of action of F1, F2, and F3 must intersect at a common point.

Question 3

A rigid body is in equilibrium under the influence of three forces F1, F2, and F3. Which of the following statements concerning the forces is/are correct?

Accepted Answer

The vector sum of the forces F1, F2, and F3 must be zero.

Accepted Answer

The moment of the forces F1, F2, and F3 about any arbitrary point must be zero.

Answer

The forces F1, F2, and F3 must be equal in magnitude.

Answer

The forces F1, F2, and F3 must act in the same direction.

Question 4

For a rigid body to be in equilibrium, what must be true about the resultant sum of forces and moments acting on it?

Accepted Answer

Zero

Answer

Non-zero

Answer

Positive

Answer

Negative

Question 5

For a rigid body to be in equilibrium, which conditions must be met?

Accepted Answer

Both the net force and the net moment acting on the body are zero.

Answer

The net force acting on the body is zero.

Answer

The net moment acting on the body is zero.

Answer

The sum of the forces and moments acting on the body is zero.

Question 6

Explain the difference between equilibrium and stability. Can an object be in equilibrium but still be unstable? Provide a clear and concise explanation.

Accepted Answer

An object is in equilibrium if the sum of all forces acting on it is zero, and stable if it returns to its equilibrium position after being slightly displaced.

Answer

Equilibrium implies stability, and vice versa.

Answer

An object in equilibrium is always stable, but an unstable object may not be in equilibrium.

Answer

Equilibrium and stability are unrelated concepts.

Question 7

Which mathematical expression correctly defines the moment about a point?

Accepted Answer

M = F × r

Answer

M = F / r

Answer

M = r × F

Answer

M = F - r

Question 8

What is the purpose of a free body diagram?

Accepted Answer

To illustrate all forces acting on an isolated body

Answer

To illustrate all moments acting on an isolated body

Answer

To illustrate all stresses within a body

Answer

To illustrate all deformations of a body

Question 9

How do you calculate the resultant force of a system of parallel forces?

Accepted Answer

Sum the magnitudes and directions of the forces

Answer

Subtract the magnitudes and directions of the forces

Answer

Multiply the magnitudes and directions of the forces

Answer

Divide the magnitudes and directions of the forces

Question 10

A rigid body is subjected to the following forces: 10 kN downwards, 5 kN upwards, 8 kN to the right, and 12 kN to the left. What is the resultant force acting on the body?

Accepted Answer

0 kN

Answer

5 kN

Answer

10 kN

Answer

18 kN

Question 11

A column is subjected to a compressive load of 100 kN. The length of the column is 2 m, and its cross-sectional area is 1000 mm2. Calculate the compressive stress in the column.

Accepted Answer

100 MPa

Answer

50 MPa

Answer

150 MPa

Answer

200 MPa

Question 12

Which condition is essential for rotational equilibrium of a rigid body?

Accepted Answer

The sum of moments about any point must be zero.

Answer

The sum of forces along any line must be zero.

Answer

The moment of inertia about any axis must be non-zero.

Answer

The center of gravity must coincide with the geometric center.

Question 13

A beam of length 8m is subjected to a uniformly distributed load of 5kN/m over its entire length. Determine the shear force at a section 2m from the left end (in kiloNewtons).

Accepted Answer

15kN

Answer

10kN

Answer

20kN

Answer

25kN

Question 14

In equilibrium analysis, which method is NOT applicable for determining forces acting on a rigid body?

Accepted Answer

Method of least squares

Answer

Method of joints

Answer

Method of sections

Answer

Principle of virtual work

Question 15

To evaluate the stability of a retaining wall against lateral earth pressure, which factors are crucial to consider?

Accepted Answer

Soil properties, wall geometry, and drainage conditions

Answer

Wall height and soil type only

Answer

Material strength and construction quality only

Answer

Statics principles are not applicable to retaining wall stability

Question 16

A floating body is in equilibrium in a fluid. Which of the following statements accurately describes the forces acting on the body?

Accepted Answer

Weight acts vertically downward through the center of gravity.

Accepted Answer

Buoyancy is a result of the pressure variation between the body's top and bottom surfaces.

Answer

Buoyancy force is always less than the weight of the body.

Answer

The center of buoyancy is always located below the center of gravity.

Question 17

For a rigid body to be in equilibrium, which of the following conditions must be satisfied?

Accepted Answer

Both (A) and (B) must be true.

Answer

The net force acting on the body must be zero.

Answer

The net moment acting on the body about any point must be zero.

Answer

Neither (A) nor (B) must be true.

Question 18

What is a free body diagram?

Accepted Answer

A diagram that illustrates all the forces acting on a body.

Answer

A diagram that illustrates all the moments acting on a body.

Answer

A diagram that shows the body's position and orientation in space.

Answer

A diagram that shows the body's velocity and acceleration.

Question 19

What is a truss?

Accepted Answer

A structure made of connected members that form a stable framework.

Answer

A structure made of connected members that can deform under load.

Answer

A structure made of connected members that are only loaded in tension or compression.

Answer

A structure made of connected members that are only loaded in bending.

Question 20

A rigid body is in equilibrium if:

Accepted Answer

The vector sum of all forces acting on the body is zero, and the vector sum of all moments acting on the body is zero.

Answer

The vector sum of all forces acting on the body is zero.

Answer

The vector sum of all moments acting on the body is zero.

Question 21

The purpose of truss analysis is to determine:

Accepted Answer

The forces in the members of the truss.

Answer

The displacements of the members of the truss.

Answer

The stresses in the members of the truss.

Question 22

The moment of inertia of a body about an axis is a measure of:

Accepted Answer

Its resistance to bending about that axis.

Answer

Its mass.

Answer

Its area.

Question 23

The bending stress in a beam subjected to a bending moment is:

Accepted Answer

Proportional to the bending moment and inversely proportional to the section modulus.

Answer

Proportional to the bending moment and proportional to the section modulus.

Answer

Proportional to the bending moment and inversely proportional to the square of the section modulus.

Question 24

The slenderness ratio of a column is a measure of its:

Accepted Answer

Susceptibility to buckling.

Answer

Stiffness.

Answer

Strength.

Question 25

The Euler formula for column buckling is used to determine:

Accepted Answer

The critical load at which a column will buckle.

Answer

The maximum load that a column can carry.

Answer

The deflection of a column under load.

Question 26

A rigid body is in equilibrium if:

Accepted Answer

The net force and net moment acting on it are zero.

Answer

The net moment acting on it is zero.

Answer

The sum of all forces acting on it is zero.

Answer

The net force acting on it is zero.

Question 27

Which of the following is NOT a type of support reaction?

Accepted Answer

Stress

Answer

Moment

Answer

Force

Answer

Shear

Question 28

The centroid of a triangle is located at:

Accepted Answer

The intersection of its medians.

Answer

The midpoint of its longest side.

Answer

The intersection of its altitudes.

Answer

The intersection of its perpendicular bisectors.

Question 29

The principle of virtual work states that:

Accepted Answer

The total work done by the forces acting on a rigid body in equilibrium is zero for any virtual displacement.

Answer

The total potential energy of a rigid body in equilibrium is zero.

Answer

The total kinetic energy of a rigid body in equilibrium is zero.

Question 30

The method of sections is used to:

Accepted Answer

Determine the internal forces in a member of a truss.

Answer

Determine the reactions at the supports of a truss.

Answer

Determine the natural frequencies of a truss.

Answer

Analyze the stability of a truss.

Question 31

The shear force in a beam:

Accepted Answer

Is the algebraic sum of the forces acting on the beam perpendicular to the beam axis.

Answer

Is the moment of the forces acting on the beam about the beam axis.

Answer

Is the product of the force and the distance from the force to the beam axis.

Answer

Is the algebraic sum of the forces acting on the beam parallel to the beam axis.

Question 32

The bending moment in a beam:

Accepted Answer

Is the algebraic sum of the moments of the forces acting on the beam about the beam axis.

Answer

Is the moment of inertia of the beam cross-section.

Answer

Is the product of the force and the distance from the force to the beam axis.

Answer

Is the algebraic sum of the forces acting on the beam perpendicular to the beam axis.

Question 33

The stress in a material is:

Accepted Answer

The force per unit area acting on the material.

Answer

The strain per unit force acting on the material.

Answer

The energy per unit volume stored in the material.

Answer

The moment per unit area acting on the material.

Question 34

Which of the following methods is commonly used to analyze the forces in the members of a truss structure?

Accepted Answer

Method of joints

Answer

Virtual work method

Answer

Method of sections

Answer

Finite element method

Question 35

A uniform rod of length L and mass M is suspended vertically from one end. Determine the tension in the rod at a distance L/4 from the suspended end.

Accepted Answer

Mg/4

Answer

Mg/2

Answer

Mg

Answer

3Mg/4

Question 36

What is the resultant force when two equal and opposite forces act on a body simultaneously?

Accepted Answer

Zero

Answer

The product of the two forces

Answer

The sum of the two forces

Answer

The difference between the two forces

Question 37

A couple is a system of two equal and opposite forces acting on a body with a perpendicular distance between their lines of action. What is the effect of a couple on a rigid body?

Accepted Answer

Rotation

Answer

No effect

Answer

Equilibrium

Answer

Translation

Question 38

Determine the moment of inertia of a rectangular area with width b and height h about an axis passing through its centroid and parallel to its width.

Accepted Answer

bh^3/12

Answer

b^3h/12

Answer

bh^3/3

Answer

b^3h/3

Question 39

A block of weight 'W' is resting on a rough inclined plane. The coefficient of friction between the block and the plane is 'μ'. At what angle of inclination will the block start to slide down the plane?

Accepted Answer

tan^(-1)μ

Answer

cos^(-1)μ

Answer

sin^(-1)μ

Answer

tan^(-1)(1/μ)

Question 40

What is the primary purpose of a truss, a structure composed of members connected at their ends to form a rigid framework?

Accepted Answer

Support and transfer loads to supports while minimizing material usage

Answer

Provide a large surface area for wind resistance

Answer

Maximize the structure's stiffness

Question 41

A rigid body is said to be in equilibrium when:

Accepted Answer

The net force acting on it is zero, and the net moment acting on it is zero.

Answer

The resultant force acting on it is zero.

Answer

The resultant moment acting on it is zero.

Question 42

In a free body diagram, forces are represented as:

Accepted Answer

Vectors with magnitude, direction, and point of application.

Answer

Scalars with only magnitude.

Answer

Vectors with only direction.

Question 43

Which of the following is NOT an equation of equilibrium for a rigid body?

Accepted Answer

F = ma

Answer

ΣM = 0

Answer

ΣF = 0

Question 44

For a beam supported at both ends and subjected to a point load at mid-span, the maximum bending moment occurs:

Accepted Answer

At the mid-span of the beam.

Answer

At a point between mid-span and a support.

Answer

At one of the supports.

Question 45

A couple is defined as:

Accepted Answer

Two equal and opposite parallel forces.

Answer

Two unequal and parallel forces.

Answer

Two equal and opposite non-parallel forces.

Question 46

The moment of inertia of a rectangular area about an axis parallel to one side, passing through its centroid, is given by:

Accepted Answer

bd³/12

Answer

bd²/12

Answer

bd³/3

Question 47

A necessary condition for a truss to be stable is that it must have:

Accepted Answer

At least three non-collinear members.

Answer

Members made of the same material.

Answer

An even number of members.

Question 48

A rigid body is in mechanical equilibrium when the resultant force acting on it is:

Accepted Answer

Zero

Answer

Non-zero and varying

Answer

Infinite

Answer

Non-zero and constant

Question 49

A free body diagram (FBD) is a representation of:

Accepted Answer

All external forces acting on a body

Answer

Moments acting on a body

Answer

Only internal forces acting on a body

Answer

Both internal and external forces acting on a body

Question 50

The moment of a force about a point is calculated as the:

Accepted Answer

Force multiplied by the perpendicular distance from the point to the line of action of the force

Answer

Force divided by the distance

Answer

Force multiplied by the parallel distance from the point to the line of action of the force

Answer

Distance multiplied by the force

Question 51

A friction force is a force that:

Accepted Answer

Always opposes the relative motion or the tendency to move between two contacting surfaces

Answer

Always acts in the direction of motion

Answer

Is independent of the direction of motion

Answer

Is perpendicular to the direction of motion

Question 52

The center of gravity (CG) of a body is the point where:

Accepted Answer

The resultant weight of the body acts

Answer

The body is most stable

Answer

The mass of the body is concentrated

Answer

The body experiences zero moments

Question 53

A couple is a system of forces that:

Accepted Answer

Produces a pure moment

Answer

Produces a pure force

Answer

Has a zero resultant force

Answer

Is always applied to a rigid body

Question 54

The fundamental equilibrium equations for a rigid body in two dimensions are:

Accepted Answer

ΣF = 0 and ΣM = 0

Answer

ΣF = 0 and ΣM = ∞

Answer

ΣF = ∞ and ΣM = 0

Answer

ΣF = M and ΣM = F

Question 55

For a rigid body to be in static equilibrium, which of the following conditions must be met?

Accepted Answer

Both the resultant force and resultant moment acting on the body must be zero.

Answer

The resultant moment acting on the body is zero, but the resultant force can be non-zero.

Answer

The resultant force acting on the body is zero, but the resultant moment can be non-zero.

Question 56

A uniform rod of length L and weight W is suspended horizontally by two vertical strings attached to its ends. What is the tension in each string?

Accepted Answer

W/2

Answer

W

Answer

W/4

Answer

2W

Question 57

A block of weight W rests on a horizontal surface with a coefficient of static friction μ. What is the minimum horizontal force required to initiate movement of the block?

Accepted Answer

μW

Answer

μW/2

Answer

W/μ

Answer

2μW

Question 58

A couple consists of two forces, equal in magnitude and opposite in direction, separated by a perpendicular distance d. What is the moment produced by this couple?

Accepted Answer

Fd

Answer

F/d

Answer

2Fd

Answer

Fd/2

Question 59

The centroid of a triangle is located at the point of intersection of which of the following?

Accepted Answer

Medians

Answer

Perpendicular bisectors of the sides

Answer

Angle bisectors

Answer

Altitudes

Question 60

For a rectangular area with base b and height h, what is its moment of inertia about its centroidal axis parallel to the base?

Accepted Answer

bh³/12

Answer

bh³/3

Answer

bh²/12

Answer

bh³/24

Question 61

A simply supported beam of length L carries a uniformly distributed load of w per unit length along its entire span.  What is the maximum bending moment in the beam?

Accepted Answer

wL²/8

Answer

wL²/16

Answer

wL²/64

Answer

wL²/32

Question 62

A truss is a structure primarily composed of which type of members?

Accepted Answer

Pin-jointed members

Answer

Welded members

Answer

Riveted members

Answer

Bolted members

Question 63

The method of sections is a technique used in structural analysis to determine what?

Accepted Answer

The internal forces in specific members of a truss

Answer

The deflection of a beam under loading

Answer

The optimal design parameters for a bridge

Answer

The overall stability of a structure

Question 64

A beam is subjected to a uniformly distributed load of 10 kN/m over a span of 5 meters. What is the equivalent point load, and at what distance from the left support should it be applied to produce the same effect?

Accepted Answer

50 kN, 2.5 meters

Answer

50 kN, 5 meters

Answer

10 kN, 2.5 meters

Answer

25 kN, 2.5 meters