Definitions [4]
Answer in one sentence.
Define strain.
The strain is defined as the ratio of change in dimensions of the body to its original dimensions.
Strain = `"change in dimensions"/"original dimensions"`
Definition: Stress
The internal restoring force per unit area of a body is called stress.
Definition: Strain
Strain is defined as the ratio of the change in dimensions of the body to its original dimensions.
Definition: Modulus of Elasticity
The modulus of elasticity of a material is the ratio of stress to the corresponding strain. It is defined as the slope of the stress-strain curve in the elastic deforming region and depends on the nature of the material.
\[\frac {stress}{strain}\] = Constant
The constant is called the modulus of elasticity.
Formulae [2]
Formula: Stress
\[\text{Stress} = \frac{\text{deforming force}}{\text{area}} = \frac{|\vec{F}|}{A}\]
- \[|\vec{F}|\] is the magnitude of the internal restoring force (which is equal to the external applied deforming force).
- A is the area over which the force acts.
- SI unit of stress: N m-2 or pascal (Pa).
- Dimensions of stress: [L-1M1T-2].
Formula: Strain
\[\text{Strain} = \frac{\text{change in dimensions}}{\text{original dimensions}}\]
Units and Dimensions of strain: Since strain is a ratio of two lengths (or two dimensions), it is a dimensionless quantity and has no unit (based on the provided formula and definition).
Important Questions [13]
- Two Wires of the Same Material Have Radii Ra and Rb Respectively. the Radius of Wire a Is Twice the Radius of Wire B. If They Are Stretched by Same Load Then Stress on Wire B is
- The Compressibility of a Substance is the Reciprocal of _________
- State Hooke’S Law. Define Elastic Limit and Modulus of Elasticity.
- The Buckling of a Beam is Found to Be More If
- Find the Initial Mass, Assuming that Hooke'S Law is Obeyed
- Young’S Modulus of Material of Wire is ‘Y’ and Strain Energy per Unit Volume is ‘E’, Then the Strain is
- Stretching of a Rubber Band Results in
- Two springs of force constants K1 and K2 (K1> K2) are stretched by same force. If W1 and W2 be the work done stretching the springs then
- Within the Elastic Limit, Find the Work Done by a Stretching Force on a Wire.
- A Mass of 1 Kg is Hung from a Steel Wire If Radius 0.5 Mm and Length 4 M. Calculate the Extension Produced. What Should Be the Area of Cross-section of the Wire So that Elastic Limit is Not Exceeded? Change in Radius is Negligible
- The Ratio of Diameters of Two Wires of the Same Material and Length is N : 1. If the Same Load is Applied to Both the Wires Then Increases in the Length of the Thin Wire is
- A and B Are Two Steel Wires and the Radius of a is Twice that of B. If They Are Stretched by the Same Load, Then the Stress on B is
- The S.I. Unit of Compressibility is
