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Chapter 1: Problem 60

Which of the following is not a unit of Young's modulus? (A) \(\mathrm{Nm}^{-1}\) (B) \(\mathrm{Nm}^{-2}\) (C) Dyne \(\mathrm{cm}^{-2}\) (D) Mega pascal

Short Answer

Expert verified
The unit that is not a measure of Young's modulus is (A) \(\mathrm{Nm}^{-1}\)

Step by step solution

01

Understanding Young's Modulus Unit

Young's modulus is a measure of the stiffness of a material, defined as the stress (force per unit area) divided by strain (proportional deformation). Therefore, its unit is a unit of force divided by a unit of area, resulting in units like pascals (Pa), gigapascals (GPa) in SI units or dyne/cm虏 in CGS units.
02

Analyzing Option A: \(\mathrm{Nm}^{-1}\)

In SI units, 'N' stands for newton, a unit of force and 'm' represents metre. The negative power indicates division. Hence, \(\mathrm{Nm}^{-1}\) refers to newton per meter which is not a force per unit area measurement. It is therefore not a correct unit for Young's modulus.
03

Analyzing Option B: \(\mathrm{Nm}^{-2}\)

\(\mathrm{Nm}^{-2}\) corresponds to newtons per square meter, or pascal (Pa), which is a proper unit for Young's modulus as it stands for force per area.
04

Analyzing Option C: Dyne \(\mathrm{cm}^{-2}\)

Dyne \(\mathrm{cm}^{-2}\) corresponds to dyne per square centimeter, a correct unit in the CGS system for Young's modulus.
05

Analyzing Option D: Mega Pascal

Mega Pascal (MPa) is another correct unit for Young's modulus. Mega is a factor of 1,000,000 and pascal is a standard unit of pressure or stress, hence force per area.

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