Import Question JSON

Current Question (ID: 19266)

Question:

$\text{A particle of mass } m \text{ is moving under a force whose delivered power } P \text{ is constant.}$ $\text{The initial velocity of the particle is zero.}$ $\text{The position of a particle at } t = 4 \text{ s is:}$

Options:

1. $\frac{16}{3} \sqrt{\frac{2P}{m}}$
2. $\frac{4}{3} \sqrt{\frac{2P}{m}}$
3. $\frac{2}{3} \sqrt{\frac{P}{m}}$
4. $\frac{3}{10} \sqrt{\frac{P}{m}}$

Solution:

$\text{We know that:}$ $P = \frac{W}{t}$ $\frac{1}{2} mv^2 = P \times t$ $v = \sqrt{\frac{2Pt}{m}} = \frac{dx}{dt}$ $x = \frac{16}{3} \sqrt{\frac{2P}{m}}$

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
}