Question

The TRUE statement is

• A. Compressibility is the reciprocal of bulk modulus
• B. The unit of Young's modulus is Nm^{-1}
• C. Dimensional formula of stress is same as that of force
• D. The unit of strain is kgm^{-2}
• E. Young's modulus of a wire depends on its length.

Answer 1

The Correct Option is A

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 \( \text{Nm}^{-1} \): This is incorrect. The unit of Young's modulus is actually \( \text{N/m}^2 \) or \( \text{Pa} \) (Pascal), which is the unit of stress, not \( \text{Nm}^{-1} \).
• Dimensional formula of stress is the same as that of force: This is incorrect. The dimensional formula of stress is \( \left[ M L^{-1} T^{-2} \right] \), which is the same as pressure, while the dimensional formula for force is \( \left[ M L T^{-2} \right] \). They are different.
• The unit of strain is \( \text{kgm}^{-2} \): 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 \( \beta = \frac{1}{B} \), where \( B \) is the bulk modulus.

Correct Answer:

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