1. State Hooke’s Law.
Within the elastic limit, stress is directly proportional to strain.
Mathematically, Stress ∝ Strain or Stress = E × Strain.
E is the modulus of elasticity.
Hooke’s law is valid only up to the elastic limit.
2. What are the moduli of elasticity and what is the relation between them?
There are three types of moduli of elasticity:
- Young’s modulus (Y)
- Bulk modulus (K)
- Rigidity modulus (G)
They describe elastic behavior under tension, volume, and shear stress respectively.
The relation between them is:
Y = 9KG / (3K + G)
3. What is Poisson’s ratio?
Poisson’s ratio is the ratio of lateral strain to longitudinal strain.
Represented as: μ = Lateral Strain / Longitudinal Strain.
It measures deformation in the transverse direction when stretched.
For most metals, μ lies between 0.25 and 0.35.
5. What are the advantages of an I-shaped girder?
- Provides high strength with less material usage.
- Has a high moment of inertia, which resists bending effectively.
- Reduces overall weight of the structure.
- Commonly used in bridges and buildings for better load-bearing capacity.
6. Define surface tension and express its units.
Surface tension is the force per unit length acting along the surface of a liquid.
It tends to minimize the surface area of the liquid.
SI unit: Newton per metre (N/m).
Dimensional formula: [M¹L⁰T⁻²].
7. Write Maxwell’s equations for free space.
- ∇·E = 0
- ∇·B = 0
- ∇×E = −∂B/∂t
- ∇×B = μ₀ε₀(∂E/∂t)
8. Define Ampere’s circuital law.
The line integral of magnetic field around a closed path is equal to μ₀ times the total current enclosed.
Mathematically: ∮ B·dl = μ₀ I.
It relates magnetic field and electric current.
It is analogous to Gauss’s law in electrostatics.
9. Write the expression for velocity of an electromagnetic wave in free space.
Velocity, c = 1 / √(μ₀ε₀).
Here, μ₀ is the permeability and ε₀ is the permittivity of free space.
The value of c ≈ 3 × 10⁸ m/s.
It represents the speed of light in vacuum.
10. What are the characteristics of Maxwell’s fourth equation?
The equation is ∇×B = μ₀ε₀ ∂E/∂t.
It shows that a changing electric field produces a magnetic field.
It forms the basis for electromagnetic wave propagation.
It demonstrates symmetry between electric and magnetic fields.