What happens to the shear modulus if the shear stress is doubled while keeping t

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Question: What happens to the shear modulus if the shear stress is doubled while keeping the shear strain constant? (2019)

Options:

Correct Answer: It remains the same

Exam Year: 2019

Solution:

Shear modulus (G) is defined as shear stress divided by shear strain. If shear strain is constant, doubling shear stress does not change G.

What happens to the shear modulus if the shear stress is doubled while keeping the shear strain constant? (2019)

What happens to the shear modulus if the shear stress is doubled while keeping the shear strain constant? (2019)

Step 1: Understand what shear modulus (G) is. It is a measure of how a material deforms under shear stress.
Step 2: Recall the formula for shear modulus: G = shear stress / shear strain.
Step 3: Identify that in this question, shear strain is kept constant.
Step 4: Note that if shear stress is doubled, the new shear stress is 2 times the original shear stress.
Step 5: Since shear strain remains the same, the formula for shear modulus becomes: G = (2 * original shear stress) / original shear strain.
Step 6: Realize that the new shear modulus is still equal to the original shear stress divided by the original shear strain, which means G does not change.
Step 7: Conclude that doubling the shear stress while keeping shear strain constant does not affect the shear modulus.

Shear Modulus – The shear modulus (G) is a measure of a material's response to shear stress, defined as the ratio of shear stress to shear strain.
Shear Stress and Shear Strain – Shear stress is the force per unit area applied parallel to the surface, while shear strain is the deformation resulting from that stress.