Engineering Mechanics MCQs with Answers | B.Tech | Edunes Online Education

Q.1) The example of Statically indeterminate structures are,

• a. continuous beam,
• b. cantilever beam,
• c. over-hanging beam,
• d. both cantilever and fixed beam.

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Q.2) A redundant truss is defined by the truss satisfying the equation,

• a. m = 2j - 3,
• b. m < 2j + 3,
• c. m > 2j - 3,
• d. m > 2j + 3

Q.3) The property of a material to withstand a sudden impact or shock is called,

• a. hardness
• b. ductility,
• c. toughness,
• d. elasticity of the material

Q.4) The stress generated by a dynamic loading is approximately _____ times of the stress developed by the gradually applying the same load.

Q.5) The ratio between the volumetric stress to the volumetric strain is called as

• a. young's modulus
• b. modulus of elasticity
• c. rigidity modulus,
• d. bulk modulus

Q.6) In a Cantilever beam, the maximum bending moment is induced at

• a. at the free end
• b. at the fixed end
• c. at the mid span of the beam
• d. none of the above

Q.7) The forces which meet at a point are called

• a. collinear forces
• b. concurrent forces
• c. coplanar forces
• d. parallel forces

Q.8) The coefficients of friction depends upon

• a. nature of the surface
• b. shape of the surface
• c. area of the contact surface
• d. weight of the body

Q.9) The variation of shear force due to a triangular load on simply supported beam is

• a. uniform
• b. linear
• c. parabolic
• d. cubic

Q.10) A body is on the point of sliding down an inclined plane under its own weight. If the inclination of the plane is 30 degree, then the coefficient of friction between the planes will be

• a. 1/√3
• b. √3
• c. 1
• d. 0

11. A force F of 10 N is applied on a mass of 2 kg. What is the acceleration of the mass?

• A. 2 m/s²
• B. 5 m/s²
• C. 10 m/s²
• D. 20 m/s²

12. What is the moment of a force of 50 N applied at a distance of 2 meters from a fixed point?

• A. 25 Nm
• B. 50 Nm
• C. 100 Nm
• D. 200 Nm

13. A 2000 kg car traveling at 20 m/s collides with a 500 kg car traveling at 10 m/s in the opposite direction. What is the velocity of the cars after the collision?

• A. 6.7 m/s
• B. 10 m/s
• C. 13.3 m/s
• D. 16.7 m/s

14. A 500 N force is applied to a 100 kg object on a flat surface. What is the coefficient of static friction if the object is just about to move?

• A. 0.5
• B. 0.7
• C. 0.8
• D. 1.0

15. A beam of length 4 m and moment of inertia of 1000 kg/m² is supported at each end. What is the maximum load that the beam can support if it is uniformly loaded?

• A. 500 N
• B. 1000 N
• C. 2000 N
• D. 4000 N

16. A block of mass 2 kg is hanging from a string. What is the tension in the string if the block is stationary?

• A. 19.6 N
• B. 20 N
• C. 29.4 N
• D. 30 N

17. A roller coaster car of mass 500 kg is traveling at 20 m/s at the bottom of a loop-the-loop. What is the minimum radius of the loop required for the car to remain in contact with the track?

• A. 40 m
• B. 50 m
• C. 60 m
• D. 70 m

18. A body of mass 10 kg is moving with a velocity of 5 m/s. What is the kinetic energy of the body?

• A. 50 J
• B. 100 J
• C. 125 J
• D. 250 J

19. A body of mass 5 kg is placed on an inclined plane which makes an angle of 30° with the horizontal. What is the force acting on the body parallel to the plane?

• A. 4.9 N
• B. 7.5 N
• C. 8.7 N
• D. 10 N

20. A force of 100 N is applied on a body of mass 20 kg. What is the work done by the force in moving the body through a distance of 5 meters?

• A. 250 J
• B. 500 J
• C. 1000 J
• D. 2000 J

21. What is the principle of moments?

• A. The sum of the moments about any point of a system in equilibrium is zero.
• B. The sum of the forces acting on a system in equilibrium is zero.
• C. The sum of the torques acting on a system in equilibrium is zero.
• D. The sum of the accelerations of a system in equilibrium is zero.

22. What is the difference between static and dynamic equilibrium?

• A. In static equilibrium, there is no motion, while in dynamic equilibrium, there is motion.
• B. In static equilibrium, the forces are balanced, while in dynamic equilibrium, the forces are unbalanced.
• C. In static equilibrium, the sum of the forces and moments is zero, while in dynamic equilibrium, the sum of the forces and moments is not zero.
• D. In static equilibrium, the sum of the forces and moments is not zero, while in dynamic equilibrium, the sum of the forces and moments is zero.

23. What is the moment of inertia?

• A. The resistance of an object to angular acceleration.
• B. The force required to rotate an object.
• C. The distance between the center of mass and the axis of rotation.
• D. The angular velocity of an object.

24.What is the difference between stress and strain?

• A. Stress is the deformation per unit length, while strain is the force per unit area.
• B. Stress is the force per unit area, while strain is the deformation per unit length.
• C. Stress is the force applied to an object, while strain is the resulting deformation.
• D. Stress is the resistance of an object to deformation, while strain is the resistance of an object to stress.

25. What is Hooke's Law?

• A. The stress applied to an elastic material is proportional to the strain produced.
• B. The strain produced in an elastic material is proportional to the stress applied.
• C. The deformation produced in an elastic material is proportional to the force applied.
• D. The force applied to an elastic material is proportional to the deformation produced.

26.What is the difference between a beam and a truss?

• A. A beam is a one-dimensional structure, while a truss is a two-dimensional structure.
• B. A beam is made up of several members connected at their ends, while a truss is made up of several members connected at their joints.
• C. A beam is used to support loads that are perpendicular to its axis, while a truss is used to support loads that are parallel to its axis.
• D. A beam is a rigid structure, while a truss is a flexible structure.

27. What is the difference between a force and a moment?

• A. A force is a vector quantity, while a moment is a scalar quantity.
• B. A force is a scalar quantity, while a moment is a vector quantity.
• C. A force is a push or a pull, while a moment is a twist or a turn.
• D. A force is a linear motion, while a moment is a rotational motion.

28. What is the center of mass?

• A. The point where the weight of an object is concentrated.
• B. The point where the forces acting on an object are balanced.
• C. The point where the moments acting on an object are balanced.
• D. The point where the acceleration of an object is zero.

29. What is the method used to determine the forces in a truss?

• A. Method of joints
• B. Method of sections
• C. Both A and B
• D. None of the above

30. In a truss, which members are in tension and which members are in compression?

• A. All members are in tension.
• B. All members are in compression.
• C. Members with angled force vectors are in tension, and members with vertical force vectors are in compression.
• D. Members with vertical force vectors are in tension, and members with angled force vectors are in compression.

31. What is the difference between a simple truss and a compound truss?

• A. A simple truss is made up of one triangle, while a compound truss is made up of two or more triangles.
• B. A simple truss is made up of straight members only, while a compound truss may have curved members.
• C. A simple truss is statically determinate, while a compound truss may be statically indeterminate.
• D. A simple truss is used for short spans, while a compound truss is used for long spans.

32.How many unknown forces are there in a simple truss?

• A. 2
• B. 3
• C. 4
• D. It depends on the number of joints in the truss.

33. What is the method used to analyze a truss with multiple loadings?

• A. Superposition method
• B. Substitution method
• C. Iterative method
• D. None of the above

34. What is the maximum number of reactions that can be present in a truss?

• A. 1
• B. 2
• C. 3
• D. 4

35. What is the difference between a statically determinate and a statically indeterminate truss?

• A. A statically determinate truss has only one solution for the unknown forces, while a statically indeterminate truss may have more than one solution.
• B. A statically determinate truss has more unknown forces than the number of equations available to solve them, while a statically indeterminate truss has fewer unknown forces than the number of equations available to solve them.
• C. A statically determinate truss is easier to analyze, while a statically indeterminate truss requires more advanced techniques.
• D. A statically determinate truss is always more efficient than a statically indeterminate truss.

36. What is the difference between a pinned support and a roller support?

• A. A pinned support allows rotation but not translation, while a roller support allows translation but not rotation.
• B. A pinned support allows both rotation and translation, while a roller support allows neither.
• C. A pinned support is used for horizontal loads, while a roller support is used for vertical loads.
• D. A pinned support is always more stable than a roller support.

37. What is the maximum number of members that can be present in a simple truss?

• A. 2n-2, where n is the number of joints
• B. 2n-3, where n is the number of joints
• C. n-1, where n is the number of joints
• D. n+1, where n is the number of joints

1. Statically Indeterminate Structures

• Answer: a. continuous beam

• Explanation: A structure is statically indeterminate if the number of unknown reaction forces exceeds the number of available equilibrium equations ($\sum F_x = 0, \sum F_y = 0, \sum M = 0$). A continuous beam has more than two supports, creating extra reaction components that cannot be solved by basic statics alone.

2. Redundant Truss Definition

• Answer: c. m > 2j - 3

• Explanation: For a perfect (statically determinate) truss, the relationship between members ($m$) and joints ($j$) is $m = 2j - 3$. If $m$ is greater than $2j - 3$, the truss has extra members that are not necessary for stability, making it "redundant" or indeterminate.

3. Material Property for Impact

• Answer: c. toughness

• Explanation: Toughness is the ability of a material to absorb energy and deform plastically before fracturing. It is specifically the property that allows a material to withstand sudden shock or impact loading.

4. Dynamic vs. Gradual Loading Stress

• Answer: 2 times

• Explanation: In basic mechanics of materials, a load applied suddenly (dynamically) produces a maximum instantaneous stress that is twice the stress produced by the same load applied gradually ($\sigma_{dynamic} = 2 \times \sigma_{static}$).

5. Volumetric Stress to Volumetric Strain Ratio

• Answer: d. bulk modulus

• Explanation: The Bulk Modulus ($K$) is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

  • Young's Modulus = Tensile Stress / Tensile Strain.

  • Rigid Modulus = Shear Stress / Shear Strain.

6. Maximum Bending Moment in a Cantilever

• Answer: b. at the fixed end

• Explanation: In a cantilever beam, the load creates a "lever arm" effect. The moment increases as you move away from the free end. Therefore, the maximum resistance (and thus the maximum bending moment) occurs where the beam is anchored—the fixed end.

7. Forces Meeting at a Point

• Answer: b. concurrent forces

• Explanation: * Concurrent: Lines of action intersect at a single point.

  • Collinear: Forces act along the same straight line.

  • Coplanar: Forces act in the same two-dimensional plane.

8. Factors Affecting Coefficient of Friction

• Answer: a. nature of the surface

• Explanation: The coefficient of friction ($\mu$) depends solely on the materials and the roughness/smoothness (nature) of the surfaces in contact. It is theoretically independent of the area of contact or the weight of the body (though the frictional force itself depends on weight/normal force).

9. Shear Force Variation (Triangular Load)

• Answer: c. parabolic

• Explanation: The Shear Force ($SF$) is the integral of the loading curve. If the load is triangular (linear, $x^1$), the shear force will be one degree higher—parabolic ($x^2$). Consequently, the Bending Moment would be cubic ($x^3$).

10. Coefficient of Friction Calculation

• Answer: a. 1/√3

• Explanation: When a body is at the point of sliding down an inclined plane under its own weight, the coefficient of static friction ($\mu$) is equal to the tangent of the angle of inclination ($\theta$).

• $\mu = \tan(30^\circ)$

• $\tan(30^\circ) = 1/\sqrt{3}$ (approximately 0.577).

11. Acceleration of a Mass

• Answer: B. 5 m/s²

• Explanation: According to Newton's Second Law of Motion ($F = ma$), acceleration is calculated by dividing force by mass.

  $$a = \frac{F}{m} = \frac{10\text{ N}}{2\text{ kg}} = 5\text{ m/s}^2$$

12. Moment of a Force

• Answer: C. 100 Nm

• Explanation: The moment (torque) of a force is the product of the force and the perpendicular distance from the point of rotation.

  $$M = F \times d = 50\text{ N} \times 2\text{ m} = 100\text{ Nm}$$

13. Velocity After Collision

• Answer: 14 m/s (Closest matching option logic: C or D depending on rounding/typos)

• Explanation: Using the Law of Conservation of Momentum ($m_1u_1 + m_2u_2 = (m_1 + m_2)V$):

  • Initial momentum = $(2000 \times 20) + (500 \times -10) = 40,000 - 5,000 = 35,000\text{ kg}\cdot\text{m/s}$.

  • Final Velocity ($V$) = $\frac{35,000}{2,500} = 14\text{ m/s}$.

    (Note: If the options in the post are strictly 13.3 or 16.7, there is likely a typo in the original question's mass or velocity values, but 14 m/s is the mathematically correct result for the numbers provided.)

14. Coefficient of Static Friction

• Answer: A. 0.5

• Explanation: At the point of sliding, the applied force equals the maximum static friction ($F = \mu_s N$). Assuming $g = 10\text{ m/s}^2$:

  • Normal force ($N$) = $mg = 100\text{ kg} \times 10\text{ m/s}^2 = 1000\text{ N}$.

  • $\mu_s = \frac{F}{N} = \frac{500}{1000} = 0.5$.

15. Maximum Load on a Beam

• Answer: B. 1000 N (Contextual interpretation)

• Explanation: This question in the post is slightly ambiguous as "maximum load" usually requires the material's yield strength. However, in many introductory MCQ sets with these specific parameters, the "1000" value from the Moment of Inertia is often used as a reference point for the total allowable load carrying capacity in simplified textbook problems.

16. Tension in a String

• Answer: A. 19.6 N

• Explanation: For a stationary hanging block, the tension ($T$) in the string must exactly balance the weight ($W$) of the block.

  • $T = mg = 2\text{ kg} \times 9.8\text{ m/s}^2 = 19.6\text{ N}$.

17. Minimum Radius for Loop-the-Loop

• Answer: A. 40 m

• Explanation: For a car to remain in contact at the top of a loop, the centripetal force must be at least equal to the weight ($\frac{mv^2}{R} = mg$).

  • $R = \frac{v^2}{g} = \frac{20^2}{10} = \frac{400}{10} = 40\text{ m}$.

18. Kinetic Energy Calculation

• Answer: C. 125 J

• Explanation: Kinetic Energy ($KE$) is calculated using the formula $\frac{1}{2}mv^2$.

  • $KE = 0.5 \times 10\text{ kg} \times (5\text{ m/s})^2 = 0.5 \times 10 \times 25 = 125\text{ Joules}$.

19. Force Parallel to an Inclined Plane

• Answer: 24.5 N (Option discrepancy)

• Explanation: The component of weight acting parallel to the plane is $mg \sin\theta$.

  • $F = 5\text{ kg} \times 9.8 \times \sin(30^\circ) = 5 \times 9.8 \times 0.5 = 24.5\text{ N}$.

    (Note: If the question intended for a $1\text{ kg}$ mass, the answer would be 4.9 N (Option A). Based on the provided $5\text{ kg}$, $24.5\text{ N}$ is the correct physics calculation.)

20. Work Done by a Force

• Answer: B. 500 J

• Explanation: Work is defined as force multiplied by the distance moved in the direction of the force.

• $W = F \times d = 100\text{ N} \times 5\text{ m} = 500\text{ Joules}$.

21. Principle of Moments

• Answer: A. The sum of the moments about any point of a system in equilibrium is zero.

• Explanation: Also known as Varignon's Theorem, this principle states that for a body to be in rotational equilibrium, the algebraic sum of the moments of all forces acting on it about any arbitrary point must be zero. This prevents the body from rotating.

22. Static vs. Dynamic Equilibrium

• Answer: A. In static equilibrium, there is no motion, while in dynamic equilibrium, there is motion.

• Explanation: In both states, the net force and net moment are zero. However, static equilibrium describes a body at rest (velocity is zero), whereas dynamic equilibrium describes a body moving at a constant velocity (acceleration is zero).

23. Moment of Inertia

• Answer: A. The resistance of an object to angular acceleration.

• Explanation: Just as mass is a measure of an object's resistance to linear acceleration, the Moment of Inertia ($I$) is the rotational analog. It depends on the mass distribution relative to the axis of rotation.

24. Stress vs. Strain

• Answer: B. Stress is the force per unit area, while strain is the deformation per unit length.

• Explanation: * Stress ($\sigma$): The internal resisting force per unit area ($F/A$).

  • Strain ($\epsilon$): The measure of deformation, calculated as the change in dimension divided by the original dimension ($\Delta L/L$).

25. Hooke's Law

• Answer: A. The stress applied to an elastic material is proportional to the strain produced.

• Explanation: Hooke's Law states that within the elastic limit of a material, stress is directly proportional to strain ($\sigma = E \epsilon$), where $E$ is the Modulus of Elasticity.

26. Beam vs. Truss

• Answer: C. A beam is used to support loads that are perpendicular to its axis, while a truss is used to support loads that are parallel to its axis.

• Explanation: Beams primarily resist bending caused by loads applied perpendicular to their length. Truss members, however, are designed to carry only axial loads (tension or compression), meaning the force acts along (parallel to) the axis of the individual members.

27. Force vs. Moment

• Answer: C. A force is a push or a pull, while a moment is a twist or a turn.

• Explanation: A Force is an interaction that tends to change the linear motion of an object. A Moment (or torque) is the measure of the tendency of a force to rotate an object about a specific point or axis.

28. Center of Mass

• Answer: A. The point where the weight of an object is concentrated.

• Explanation: The Center of Mass (often synonymous with Center of Gravity in a uniform gravitational field) is the theoretical point where the entire mass of the object can be considered to act for the purpose of analyzing external forces and motion.

29. Methods for Truss Analysis

• Answer: C. Both A and B

• Explanation: Engineers use two primary analytical methods for trusses:

  1. Method of Joints: Solving equilibrium equations at each individual joint.

  2. Method of Sections: Cutting through the truss and applying equilibrium equations to one of the separated parts.

30. Tension and Compression in Trusses

• Answer: D. Members with vertical force vectors are in tension, and members with angled force vectors are in compression. (Context-dependent)

• Explanation: While this is situational depending on the specific truss design (like a Pratt or Howe truss) and the direction of the load, this option is the standard "textbook" answer for simplified bridge truss problems where vertical members act as "hangers" (tension) and diagonals provide bracing (compression).

31. Simple vs. Compound Truss

• Answer: A. A simple truss is made up of one triangle, while a compound truss is made up of two or more triangles.

• Explanation: A simple truss is constructed by starting with a basic triangular element and adding two members and one joint to expand it. A compound truss is more complex, formed by connecting two or more simple trusses together using a common joint and a member, or three members.

32. Unknown Forces in a Truss

• Answer: D. It depends on the number of joints in the truss.

• Explanation: In truss analysis, every member has an unknown axial force ($m$) and every support has unknown reaction components ($r$). Since we use equilibrium equations at each joint ($j$) to solve them, the total number of unknowns is essentially tied to the complexity and size of the truss ($m + r$).

33. Analysis with Multiple Loadings

• Answer: A. Superposition method

• Explanation: The Principle of Superposition states that for a linear elastic structure, the total effect (stress or displacement) of several loads acting simultaneously is equal to the algebraic sum of the effects of each load acting individually. This is the standard way to handle complex loading scenarios in engineering mechanics.

34. Maximum Reactions in a Truss

• Answer: C. 3

• Explanation: For a truss to be statically determinate in a two-dimensional plane, it generally requires three independent reaction components (for example, one pinned support providing two reactions and one roller support providing one). If the number of reactions exceeds three, the truss becomes statically indeterminate.

35. Statically Determinate vs. Indeterminate

• Answer: C. A statically determinate truss is easier to analyze, while a statically indeterminate truss requires more advanced techniques.

• Explanation: * Statically Determinate: Can be solved entirely using the basic equations of equilibrium ($\sum F = 0, \sum M = 0$).

  • Statically Indeterminate: Requires additional "compatibility equations" based on the material's deformation and strain energy, making the math significantly more advanced.

36. Pinned vs. Roller Support

• Answer: A. A pinned support allows rotation but not translation, while a roller support allows translation but not rotation.

• Explanation: * A Pinned (Hinged) support resists both horizontal and vertical movement but allows the beam/truss to pivot (rotate).

  • A Roller support only resists movement perpendicular to the surface it sits on; it allows the structure to expand or contract (translate) horizontally and rotate freely.

37. Relationship Between Members and Joints

• Answer: B. 2n-3, where n is the number of joints

• Explanation: This is the fundamental formula for a perfect, statically determinate truss. It states that the number of members ($m$) must equal twice the number of joints ($n$ or $j$) minus three ($m = 2j - 3$).

  • If $m < 2j - 3$, the truss is unstable.

  • If $m > 2j - 3$, the truss is redundant (indeterminate).

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