Modulus of Resilience

The modulus of resilience is a mechanical property that measures the ability of a material to absorb elastic strain energy without undergoing permanent deformation or failure. It provides valuable information about the material's strength and toughness, which are crucial considerations in engineering design.

Definition

The modulus of resilience is defined as the ratio of the proof resilience to unit volume of the material. Proof resilience is the maximum energy that a material can absorb per unit volume without permanent deformation.

Proof Resilience

Proof resilience is the area under the stress-strain curve up to the elastic limit of the material. It represents the energy that can be absorbed by the material without causing permanent deformation. The stress-strain curve is obtained from a tensile test, where the material is subjected to increasing tensile forces until it reaches its breaking point.

Calculation

To calculate the modulus of resilience, the proof resilience is divided by the unit volume of the material. The unit volume is typically represented in cubic meters or cubic millimeters, depending on the system of units used.

Significance

The modulus of resilience provides important information about the ability of a material to withstand high impact or shock loading conditions. It is a measure of the material's ability to absorb energy without undergoing plastic deformation or failure.

Comparison with Other Options

Option a) states that the modulus of resilience is the ratio of maximum stress energy and unit volume. However, maximum stress energy is not the correct parameter to consider when calculating the modulus of resilience.

Option b) states that the modulus of resilience is the ratio of maximum strain energy and unit volume. While strain energy is related to resilience, the maximum strain energy is not the correct parameter to consider. The modulus of resilience is based on the proof resilience, which is obtained from the stress-strain curve.

Option c) correctly states that the modulus of resilience is the ratio of proof resilience and unit volume. This is the correct definition and calculation for the modulus of resilience.

Option d) incorrectly states that the modulus of resilience is the ratio of proof resilience and unit area. Unit volume, not unit area, is the appropriate parameter to consider when calculating the modulus of resilience.

Conclusion

In conclusion, the correct statement for the modulus of resilience is option c) - it is the ratio of proof resilience and unit volume. The modulus of resilience provides valuable information about a material's ability to absorb elastic strain energy without permanent deformation or failure.