Topics covered in Paper I of the Mechanical Engineering Optional Subject:

1. Engineering Mechanics:
Engineering Mechanics is the branch of mechanics that deals with the behavior of physical bodies when subjected to various types of forces and the analysis of motion and deformation. The topics covered in this section include:

- Statics: Equilibrium of particles and rigid bodies, analysis of trusses, frames, and beams.
- Dynamics: Laws of motion, work and energy, power and efficiency, impulse and momentum, and impact.

2. Strength of Materials:
Strength of Materials is the study of the behavior of solid objects under external loads. It involves analyzing the stresses and strains in different materials and determining their mechanical properties. The topics covered in this section include:

- Stress and strain: Types of stress and strain, Hooke's law, thermal stresses.
- Principal stresses and strains: Mohr's circle, theories of failure.
- Bending moment and shear force diagrams: Deflection of beams, torsion of circular shafts.
- Columns and struts: Euler's theory, crippling loads, and Rankine's formula.

3. Theory of Machines:
Theory of Machines is concerned with the study of machines and mechanisms that are used to transmit and convert motion and force. The topics covered in this section include:

- Kinematics of machines: Velocity and acceleration analysis, gear trains, and cam mechanisms.
- Dynamics of machines: Flywheels, balancing of rotating and reciprocating masses, gyroscopes.
- Vibrations: Free and forced vibrations, critical speeds of shafts, and whirling of shafts.

4. Machine Design:
Machine Design involves the creation of new or modified mechanical components or systems, considering factors such as functionality, reliability, and manufacturability. The topics covered in this section include:

- Design of machine elements: Design of shafts, gears, bearings, springs, clutches, and brakes.
- Design for manufacturing: Tolerances, fits, and surface roughness.
- Design of jigs and fixtures: Principles and applications.

5. Fluid Mechanics:
Fluid Mechanics is the study of fluids and their behavior under various conditions. It involves analyzing the forces acting on fluids and their flow characteristics. The topics covered in this section include:

- Fluid properties: Density, viscosity, and surface tension.
- Fluid statics: Pressure measurement, buoyancy, and stability of floating bodies.
- Fluid dynamics: Bernoulli's equation, flow through pipes, and boundary layer theory.

Overall, Paper I of the Mechanical Engineering Optional Subject covers a wide range of topics related to mechanics, materials, machine design, and fluid mechanics. A strong understanding of these topics is essential for aspiring mechanical engineers to excel in their field.