Import Question JSON

Current Question (ID: 8751)

Question:

$\text{Given the equation } \left(P + \frac{a}{V^2}\right)(V - b) = \text{constant}. \text{ The units of } a \text{ will be: (where } P \text{ is pressure and } V \text{ is volume)}$

Options:

1. $\text{dyne} \times \text{cm}^5$
2. $\text{dyne} \times \text{cm}^4$
3. $\text{dyne}/\text{cm}^3$
4. $\text{dyne}/\text{cm}^2$

Solution:

$\text{Hint: Use the principle of homogeneity of dimensions.}$ $\text{Step: Find the units of } a.$ $\text{By using dimensional analysis, addition or subtractions is only possible for quantities having the same dimensions.}$ $[P] = \frac{[a]}{[V]^2}$ $\Rightarrow [a] = [PV^2]$ $\Rightarrow [a] = \frac{\text{Force}}{\text{Area}} \times (\text{Volume})^2 = \text{Force} \times \frac{(L^3)^2}{L^2}$ $\Rightarrow [a] = \text{Force} \times (\text{Length})^4$ $\Rightarrow [a] = \text{dyne} \times (\text{cm})^4$ $\text{Hence, option (2) is the correct answer.}$

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
}