Import Question JSON

Current Question (ID: 9921)

Question:

$\text{A particle of mass m is moving in a circular path with a speed } v = kt, \text{ where k is constant and t is time. The instantaneous power delivered to the particle is:}$

Options:

1. $\text{Zero}$
2. $mkt$
3. $mk^2t$
4. $mk^2t^2$

Solution:

\text{The instantaneous power delivered to the particle is calculated as the product of the tangential force and the instantaneous speed.} \text{Given the speed } v = kt\text{, the tangential acceleration is } a_t = \frac{dv}{dt} = k\text{.} \text{The tangential force is } F_t = ma_t = mk\text{.} \text{Therefore, the instantaneous power } P = F_t \cdot v = (mk)(kt) = mk^2t\text{.}

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
}