(SEM III) THEORY EXAMINATION 2023-24 ENGINEERING MECHANICS

This examination assesses a student's understanding of the fundamental principles of Engineering Mechanics, including force systems, moments, equilibrium, centroids, moment of inertia, trusses, kinetics, kinematics, and methods such as virtual work. The questions evaluate both conceptual clarity and problem-solving ability essential for all engineering branches.

The paper is divided into three structured sections, covering basic theory, applied mechanics, and analytical problem solving.

SECTION A – Short Answer Questions (14 Marks)

Seven questions × 2 marks each

This section tests foundational definitions and essential formulas used throughout engineering mechanics.

Topics Included:

1. Classifications of Engineering Mechanics

Statically vs dynamically, particles vs rigid bodies, deformable bodies.

2. Types of Force Systems

Coplanar, non-coplanar, concurrent, non-concurrent, collinear, parallel.

3. Centroid Coordinates

General formula using integration or area moments:

xˉ=∫xdA∫dA,yˉ=∫ydA∫dA\bar{x}=\frac{\int x dA}{\int dA},\quad \bar{y}=\frac{\int y dA}{\int dA}xˉ=∫dA∫xdA​,yˉ​=∫dA∫ydA​

4. Mass Moment of Inertia of Solid Sphere

Using standard formula:

I=25MR2I = \frac{2}{5} M R^2I=52​MR2

5. Equilibrium Equations for 3D System

ΣFx=0,  ΣFy=0,  ΣFz=0ΣMx=0,  ΣMy=0,  ΣMz=0\Sigma F_x = 0, \; \Sigma F_y = 0, \; \Sigma F_z = 0 \Sigma M_x = 0, \; \Sigma M_y = 0, \; \Sigma M_z = 0ΣFx​=0,ΣFy​=0,ΣFz​=0ΣMx​=0,ΣMy​=0,ΣMz​=0

6. Law of Conservation of Energy

Energy cannot be created or destroyed; only transformed.

7. Virtual Displacement

A small imaginary change in configuration consistent with constraints.

This section checks command over definitions, formulas, and core principles.

SECTION B – Applied Concepts & Problem-Based Questions (21 Marks)

Attempt any three questions – each 7 marks

This section evaluates the student’s ability to apply fundamentals to engineering structures, force systems, trusses, motion, and virtual work.

Questions Covered:

1. Systems of Forces & Applications

Definition of a force system, real-world applications (frames, machines, structures, vehicles).

2. Moment of Inertia of Complex Area

Calculation of second moment of area about a given axis AB using standard geometric formulas.

3. Plane Truss – Assumptions & Analysis

• Loads at joints
• Members connected by pin joints
• No bending moment
• Methods: joint method, section method

4. Equation of Motion Using Integration

Deriving:

F=mdvdt,∫a dt=v,∫v dt=sF = m \frac{dv}{dt},\quad \int a \, dt = v,\quad \int v \, dt = sF=mdtdv​,∫adt=v,∫vdt=s

5. Virtual Work Method for Spring System

Deriving equilibrium conditions for angle θ and tension using δW = 0 principle.

This section emphasizes engineering reasoning and mathematical formulation.

SECTION C – Long Analytical / Numerical Questions (35 Marks)

Each question contains two options. Students must attempt one.

3. Resultant of Forces / Wedge Mechanism (7 Marks)

Option A – Resultant of Four Forces

Compute magnitude and direction using:

Rx=ΣFcos⁡θ,Ry=ΣFsin⁡θ,R=Rx2+Ry2R_x=\Sigma F\cos\theta,\quad R_y=\Sigma F\sin\theta,\quad R=\sqrt{R_x^2+R_y^2}Rx​=ΣFcosθ,Ry​=ΣFsinθ,R=Rx2​+Ry2​​

Option B – Wedge & Equilibrium

Definition of wedge; analysis of lifting/ separating bodies; frictional force equations.

4. Centroid & Moment of Inertia (7 Marks)

Option A – Centroid of Circular Section

Finding centroid using symmetry and integration.

Option B – Mass Moment of Inertia of Solid Cylinder

Deriving formulas for:
• Longitudinal axis
• Centroidal transverse axis

5. Truss Forces / Beam Reactions (7 Marks)

Option A – Truss Analysis

Finding forces in members using:
• Method of joints
• Resolution of forces
• Identifying tension & compression

Option B – Reactions in Overhanging Beam

Calculating RA and RB using equilibrium equations:

ΣM=0,ΣFy=0\Sigma M=0, \Sigma F_y=0ΣM=0,ΣFy​=0 

6. Kinematics of Translation & Rotation (7 Marks)

Option A – Non-uniform Acceleration of Ship

Acceleration proportional to v2v^2v2; integrate using:

a=kv2,  a=dvdta = k v^2 ,\; a = \frac{dv}{dt}a=kv2,a=dtdv​

Option B – Flywheel Retardation & Slowdown

Convert rpm → rad/s, compute angular acceleration and total revolutions.

7. Kinetics of Rigid Body / Flywheel Work (7 Marks)

Option A – Terminologies in Kinetics

Mass, inertia, angular velocity, angular acceleration, torque, momentum, impulse.

Option B – Work Done & Increase in KE for Flywheel

Using:

W=ΔKE=12I(ω22−ω12)W = \Delta KE = \frac{1}{2} I(\omega_2^2 - \omega_1^2)W=ΔKE=21​I(ω22​−ω12​)