A metallic cube is subjected to equal pressure (P) on its all the six ...
When a body is subjected to the identical stress σ in three mutually perpendicular directions, the body undergoes uniform changes in three directions without the distortion of the shape.
The ratio of change in volume to original volume is defined as volumetric strain (ϵ
V).
Bulk modulus (K)
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A metallic cube is subjected to equal pressure (P) on its all the six ...
Bulk modulus is the correct answer (option C).
Bulk modulus is a measure of a material's resistance to uniform compression. It quantifies the ratio of applied pressure to the resulting volumetric strain. When a metallic cube is subjected to equal pressure on all its six faces, it undergoes a uniform compression in all directions.
In this scenario, the pressure (P) applied to the cube is the same on all six faces. As a result, the cube experiences a decrease in volume, which is known as volumetric strain (Vis). The volumetric strain is defined as the change in volume divided by the original volume of the cube.
Now, let's understand why option C, which is the bulk modulus, is the correct choice for the ratio P/Vis.
Key Points:
- Elastic modulus measures the material's resistance to deformation along a specific axis or direction, such as tension or compression. It is not directly related to volumetric strain.
- Shear modulus measures the material's resistance to deformation caused by shear stress, which is a force applied parallel to the material's surface. It is not directly related to volumetric strain.
- Strain energy per unit volume is a measure of the energy stored in a material due to deformation. It is not directly related to the ratio of pressure to volumetric strain.
Explanation:
1. Bulk modulus is defined as the ratio of applied pressure to the resulting volumetric strain. It quantifies how a material's volume changes under uniform compression.
2. In this scenario, the metallic cube is subjected to equal pressure on all six faces. This uniform compression causes a decrease in volume.
3. The volumetric strain (Vis) is given by the formula Vis = (ΔV/V), where ΔV is the change in volume and V is the original volume of the cube.
4. The pressure (P) applied to the cube is the same on all six faces, and it is the force per unit area. Therefore, P = F/A, where F is the force and A is the area of each face.
5. The ratio P/Vis can be written as (F/A)/(ΔV/V).
6. By rearranging the terms, we get P/Vis = (F/V)/(ΔV/A).
7. (F/V) represents the original stress, which is the force per unit original volume of the cube.
8. (ΔV/A) represents the strain, which is the change in volume per unit area.
9. Therefore, the ratio P/Vis can be simplified as the stress/strain ratio, which is the definition of the bulk modulus.
10. Hence, the correct answer is option C, the bulk modulus.
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