Import Question JSON

Current Question (ID: 8736)

Question:

$\text{If force (F), velocity (v), and time (T) are taken as fundamental units, the dimensions of mass will be:}$

Options:

1. $[FvT^{-1}]$
2. $[FvT^{-2}]$
3. $[Fv^{-1}T^{-1}]$
4. $[Fv^{-1}T]$

Solution:

$\text{Hint: } F = ma$ $\text{Step: Express the mass in terms of F, v and T.}$ $\text{From Newton's second law: } F = ma \Rightarrow m = \frac{F}{a}$ $\text{Since acceleration } a = \frac{v}{T} \text{ (change in velocity over time):}$ $m = \frac{F}{a} = \frac{F}{\frac{v}{T}} = \frac{FT}{v} = [Fv^{-1}T]$ $\text{Therefore, when F, v, and T are fundamental units, mass has dimensions } [Fv^{-1}T]\text{.}$ $\text{Hence, option (4) is the correct answer.}$

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
}