- **Stress-strain relationship**: It is the relation between the stress (force per unit area) applied to a material and the strain (change in dimension) produced in the material. 

- **Hooke’s law**: It is the law that states that for small deformations, the stress is proportional to the strain. Mathematically, it can be written as $$\sigma = E \epsilon$$ where $\sigma$ is the stress, $E$ is the modulus of elasticity, and $\epsilon$ is the strain. 

**Young modulus**: It is the modulus of elasticity for longitudinal stress and strain. It measures the stiffness of a material. It is defined as the ratio of longitudinal stress to longitudinal strain. - 

**Bulk modulus**: It is the modulus of elasticity for volumetric stress and strain. It measures the compressibility of a material. It is defined as the ratio of volumetric stress to volumetric strain. 

- **Shear modulus**: It is the modulus of elasticity for tangential stress and strain. It measures the rigidity of a material. It is defined as the ratio of tangential stress to tangential strain. 

- **Modulus of rigidity**: It is another name for shear modulus. 

- **Poisson’s ratio**: It is the ratio of lateral strain to longitudinal strain for a material under longitudinal stress. It measures the degree of contraction or expansion of a material in a direction perpendicular to the applied force. 

- **Elastic energy: It is the potential energy stored in a material due to its deformation by an external force. It is equal to the work done by the force to deform the material. -

Pressure due to a fluid column: It is the pressure exerted by a fluid at a given depth due to the weight of the fluid above it. It is given by the formula $$P = \rho g h$$ where $P$ is the pressure, $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity, and $h$ is the depth of the fluid.

 Pascal’s law: It is the law that states that the pressure applied to an enclosed fluid is transmitted equally to every part of the fluid and the walls of the container.

 Applications of Pascal’s law: Pascal’s law can be used to explain the working of hydraulic devices such as hydraulic lift and hydraulic brakes. A hydraulic lift consists of two pistons of different cross-sectional areas connected by a pipe filled with a fluid. When a small force is applied to the smaller piston, it creates a pressure that is transmitted to the larger piston. Since the pressure is the same, the force on the larger piston is greater than the force on the smaller piston by a factor equal to the ratio of the areas of the pistons. This allows the larger piston to lift a heavy load with a small input force. A hydraulic brake consists of a brake pedal, a master cylinder, and four brake cylinders connected by pipes filled with a fluid. When the brake pedal is pressed, it creates a pressure in the master cylinder that is transmitted to the brake cylinders. The brake cylinders then apply a force on the brake pads that clamp the wheels and stop the vehicle. 

Effect of gravity on fluid pressure: Gravity affects the pressure of a fluid by creating a pressure gradient. The pressure of a fluid increases with depth due to the weight of the fluid above it. The pressure difference between two points in a fluid is given by $$\Delta P = \rho g \Delta h$$ where $\Delta P$ is the pressure difference, $\rho$ is the density of the fluid, $g$ is the acceleration due to gravity, and $\Delta h$ is the difference in height between the two points.