Import Question JSON

Current Question (ID: 10352)

Question:

Given below are two statements: Assertion (A): Hooke's law is applicable up to the elastic limit. Reason (R): Up to the elastic limit, stress is directly proportional to strain.

Options:

1. Both (A) and (R) are True and (R) is the correct explanation of (A).
2. Both (A) and (R) are True but (R) is not the correct explanation of (A).
3. (A) is True but (R) is False.
4. Both (A) and (R) are False.

Solution:

Hint: Hooke's law is applicable up to the proportionality limit. Explanation: Let's analyze the statements logically. Assertion (A): Hooke's law is applicable up to the elastic limit. Hooke's law is valid only within the proportional limit, which is the region where stress is directly proportional to strain. However, the proportional limit is usually slightly below the elastic limit. Beyond the proportional limit, stress is no longer proportional to strain, but the material can still return to its original shape (i.e., it remains elastic) until the elastic limit is reached. So, Hooke's law is not applicable throughout the entire elastic region but only up to the proportional limit. So the Assertion (A) is false. Reason (R): Up to the elastic limit, stress is directly proportional to strain. This statement is only valid up to the proportionality limit. Beyond the proportionality limit (but still within the elastic region), stress and strain no longer maintain a linear relationship. So the Reason (R) is false. Since both the assertion and reason contain inaccuracies, both statements are false. Hence, option (4) is the correct answer.

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}