Question

The following figure shows a region in which rocks in areas A, B and C follow Hooke's law and are subject to the same stress. B exhibits lower strain than both A and C. What can we infer about the nature of B?

 

• A. B is part of a plate boundary
• B. B has higher heat flow values compared to A and C
• C. B is made up of rocks of lower density compared to A and C
• D. B is made up of rocks that have higher strength compared to A and C

Hint:

Remember Hooke's Law: For a given stress, a material with a higher Young's Modulus will exhibit lower strain, indicating higher stiffness and generally higher strength.

Answer 1

The Correct Option is D

Step 1: Understanding Hooke's Law and its relation to stress and strain.
Hooke's Law states: \[ {Stress} = {Young's Modulus} \times {Strain} \] \[ \sigma = E \epsilon \] where \( \sigma \) is stress, \( E \) is Young's Modulus, and \( \epsilon \) is strain. 
Step 2: Analyzing the given conditions.
Given that the stress is the same in areas A, B, and C (\( \sigma_A = \sigma_B = \sigma_C = \sigma \)), and the strain in B is lower than in A and C (\( \epsilon_B<\epsilon_A \) and \( \epsilon_B<\epsilon_C \)). From Hooke's Law: \[ E_A = \frac{\sigma}{\epsilon_A}, \quad E_B = \frac{\sigma}{\epsilon_B}, \quad E_C = \frac{\sigma}{\epsilon_C} \] Since \( \epsilon_B \) is the smallest, \( E_B \) must be the largest (\( E_B>E_A \) and \( E_B>E_C \)). 
Step 3: Relating Young's Modulus to the strength of rocks. Young's Modulus is a measure of a material's stiffness or resistance to elastic deformation under stress. A higher Young's Modulus indicates a stiffer and generally stronger material that will exhibit less strain under the same stress. 
Step 4: Evaluating the options.
(A) Plate boundaries can have various stress and strain regimes, so this doesn't directly imply lower strain.
(B) Higher heat flow usually weakens rocks, leading to higher strain under the same stress.
(C) Density is not directly related to the stress-strain relationship described by Hooke's Law.
(D) Higher strength in rocks implies a higher resistance to deformation, hence lower strain under the same stress. This aligns with B having a higher Young's Modulus.