Import Question JSON

Current Question (ID: 8754)

Question:

$\text{The quantities } A \text{ and } B \text{ are related by the relation, } m = \frac{A}{B}, \text{ where } m \text{ is the linear density and } A \text{ is the force. The dimensions of } B \text{ are of:}$

Options:

1. $\text{Pressure}$
2. $\text{Work}$
3. $\text{Latent heat}$
4. $\text{None of the above}$

Solution:

\text{Hint: } m = \text{linear density} = \text{mass per unit length} = \frac{M}{L} \\[0.5em] \text{Step: Find the dimension of } B \\[0.5em] \text{According to the question: } m = \frac{A}{B} \text{ where } A \text{ is the force} \\[0.3em] m \text{ is linear density} = \frac{M}{L} \\[0.5em] [A] = [MLT^{-2}] \\[0.3em] [m] = [ML^{-1}] \\[0.5em] \text{So, } [B] = \frac{[A]}{[m]} = \frac{[MLT^{-2}]}{[ML^{-1}]} = [L^2T^{-2}] \\[0.5em] \text{Therefore, the dimensions of } B \text{ are the same as latent heat.} \\[0.3em] \text{Hence, option (3) 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
}