Consider the following statements regarding mechanical properties of solids : 1. The ratio of tensile stress to longitudinal strain is defined as bulk modulus. 2. The ratio of hydraulic stress to corresponding hydraulic strain is called Young's modulus. 3. The ratio of shearing stress to corresponding shearing strain is called modulus of rigidity. Which of the statements given above is/are correct?

In the study of mechanical properties of solids, Young's modulus is defined as the ratio of tensile (or compressive) stress to longitudinal strain. Statement 1 is incorrect because it incorrectly attributes this ratio to the bulk modulus. The bulk modulus is actually the ratio of hydraulic (volumetric) stress to the corresponding hydraulic (volumetric) strain, which measures a substance's resistance to compression. Consequently, Statement 2 is also incorrect as it swaps the definition of Young's modulus with hydraulic stress. Statement 3 is correct; the modulus of rigidity, also known as the shear modulus, is defined as the ratio of shearing stress to the corresponding shearing strain. While the provided snippets discuss shear stresses in the context of geomorphic processes and rock fracture [3], standard physical principles confirm that only the third statement accurately matches the definition of the specific elastic modulus mentioned.

Sources

1. [1] FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.) > Chapter 5: Geomorphic Processes > EXOGENIC PROCESSES > p. 39
2. [2] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 6: Geomorphic Movements > Physical Weathering Processes > p. 83
3. [3] FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI (NCERT 2025 ed.) > Chapter 5: Geomorphic Processes > Physical Weathering Processes > p. 41