Import Question JSON

Current Question (ID: 10412)

Question:

\text{Given below are two statements:} \text{Assertion (A): Bulk modulus of elasticity } B \text{ represents the incompressibility of the material.} \text{Reason (R): } B = -\frac{\Delta p}{\Delta V/V}\text{, where symbols have their usual meaning.}

Options:

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

Solution:

\text{Assertion (A): Bulk modulus of elasticity } B \text{ represents the incompressibility of the material.} \text{The bulk modulus (}B\text{) measures a substance's resistance to compression under pressure. A higher bulk modulus indicates that a material is more difficult to compress, meaning it is more incompressible. Therefore, this statement is True.} \text{Reason (R): } B = -\frac{\Delta p}{\Delta V/V}\text{, where symbols have their usual meaning.} \text{The definition of bulk modulus is indeed the ratio of the change in pressure (}\Delta p\text{) to the fractional change in volume (}\Delta V/V\text{), with a negative sign to account for the fact that an increase in pressure leads to a decrease in volume (and vice-versa), ensuring } B \text{ is positive. So, this statement is True.} \text{Relationship between (A) and (R):} \text{The definition of the bulk modulus (R) directly explains why it represents the incompressibility of a material (A). A larger } B \text{ means a larger pressure change is required for a given fractional volume change, implying greater resistance to compression or higher incompressibility. Therefore, (R) is the correct explanation of (A).} \text{Based on this analysis, both (A) and (R) are true, and (R) is the correct explanation of (A).} \text{The final answer is option 1.}

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
}