Import Question JSON

Current Question (ID: 18978)

Question:

$\text{An expression for a dimensionless quantity } P \text{ is given by}$ $P = \frac{\alpha}{\beta} \log_e \left( \frac{kt}{\beta x} \right);$ $\text{where } \alpha \text{ and } \beta \text{ are constants, } x \text{ is distance; } k \text{ is Boltzmann constant and } t \text{ is the temperature.}$ $\text{Then the dimension of } \alpha \text{ will be:}$

Options:

1. $[M^0 L^{-1} T^0]$
2. $[ML^0 T^{-2}]$
3. $[MLT^{-2}]$
4. $[ML^2 T^{-2}]$

Solution:

$\text{Since } P \text{ is dimensionless, the argument of the logarithm must also be dimensionless.}$ $\text{Thus, } \frac{kt}{\beta x} \text{ is dimensionless.}$ $\text{The dimension of } k \text{ is } [ML^2 T^{-2} K^{-1}].$ $\text{The dimension of } t \text{ is } [K].$ $\text{The dimension of } x \text{ is } [L].$ $\text{Therefore, the dimension of } \alpha \text{ must be } [MLT^{-2}].$

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
}