Import Question JSON

Current Question (ID: 8745)

Question:

$\text{An object is moving through a liquid. The viscous damping force acting on it is proportional to the velocity. Then the dimensions of the constant of proportionality are:}$

Options:

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

Solution:

$\text{Hint: } [F] = [MLT^{-2}]$ $\text{Step: Find the dimensions of the proportionality constant.}$ $\text{According to the question; } F \propto v$ $\Rightarrow F = kv \Rightarrow [k] = \frac{[F]}{[v]} = \frac{[MLT^{-2}]}{[LT^{-1}]} = [MT^{-1}]$ $\text{Therefore, the dimensions of the proportionality constant are } [ML^0T^{-1}].$ $\text{Hence, option (4) is the correct answer.}$

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
}