How much should the pressure on a litre of water be changed to compress it by $0.10\%$?

(i) The deforming force acting on a body per unit area of the body is called stress i.e. stress $\frac{F}{A}$

(ii) Normal stress $= \frac{ \text{Force acting perpendicular to the surface of the body} }{ \text{Area of cross-section of the body} }= \frac{F_{\perp }}{A}$

(iii) Tangential stress $= \frac{\text{ Force acting tangential to the surface of the body }}{\text{ Area of cross-section of the body }}= \frac{F_{\parallel }}{A}$

2. Strain:

(i) Longitudinal strain $= \frac{\text{Change in length of body} }{ \text{Original volume of body} }= \frac{\mathrm{\Delta }l}{l}$

(ii) Volume strain $= \frac{ \text{Change in volume of body} }{ \text{Original volume of body} }= \frac{\mathrm{\Delta }V}{V}$

3. Shear strain:

It is defined as the angle through which a vertical face of a body is displaced when tangential force is applied on it.

4. Hooke's law:

(i) According to this law, within the elastic limit, stress is directly proportional to the strain.

(ii) Modulus of elasticity is defined as the ratio of the stress to the strain.

5. Types of modulus of elasticity:

(i) Young's modulus of elasticity is defined as the ratio of the normal stress to the longitudinal strain. $Y= \frac{\frac{F}{A}}{\frac{\mathrm{\Delta }l}{l}}= \frac{Fl}{A\mathrm{\Delta }l}$

(ii) Bulk modulus of elasticity is defined as the ratio of the normal stress to the volume strain. $B= \frac{\mathrm{\Delta }P}{\frac{\mathrm{\Delta }V}{V}}= \frac{V\mathrm{\Delta }P}{\mathrm{\Delta }V}$

(iii) Compressibility is the reciprocal of the bulk modulus of elasticity.

(iv) Modulus of rigidity is defined as the ratio of the tangential stress to the shear strain.

6. Poisson's ratio:

It is defined as the ratio of the lateral strain to the longitudinal strain.

7. Elastic potential energy:

Energy stored per unit volume of a stretched wire is given by $U= \frac{1}{2}\times \mathrm{Stress}\times \mathrm{Strain}$