Elastic Moduli

When a body is strained, the energy stored per unit volume (also known as the strain energy density) is related to the stress and strain through Young's modulus .

The formula for the energy stored per unit volume is derived from the relationship between stress and strain, and it is given by: Since stress ( ) is related to Young's modulus ( ) and strain ( ) by: Therefore, strain ( ) can be written as: Substituting this into the energy formula: Thus, the energy stored per unit volume is:

Correct Answer:

Correct Answer: (E)

Let's analyze each statement to identify the correct one:

• Young's modulus of a wire depends on its length: This statement is incorrect. Young's modulus is a material property, and it does not depend on the length of the wire. It only depends on the material's properties such as its elastic nature and the cross-sectional area.
• The unit of Young's modulus is : This is incorrect. The unit of Young's modulus is actually or (Pascal), which is the unit of stress, not .
• Dimensional formula of stress is the same as that of force: This is incorrect. The dimensional formula of stress is , which is the same as pressure, while the dimensional formula for force is . They are different.
• The unit of strain is : This is incorrect. Strain is a dimensionless quantity, as it represents a ratio of change in length to the original length, so it has no units.
• Compressibility is the reciprocal of bulk modulus: This statement is correct. Compressibility is the inverse of the bulk modulus, and it measures the relative change in volume per unit change in pressure. The formula for compressibility is , where is the bulk modulus.

Correct Answer:

Correct Answer: (A) Compressibility is the reciprocal of bulk modulus