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=52MR2
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=ΣFcosθ,Ry=ΣFsinθ,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=21I(ω22−ω12)
