Import Question JSON

Current Question (ID: 8844)

Question:

$\text{A particle moves a distance } x \text{ in time } t \text{ according to equation } x = (t + 5)^{-1}\text{. The acceleration of the particle is proportional to:}$

Options:

1. $(\text{velocity})^{\frac{3}{2}}$
2. $(\text{distance})^{2}$
3. $(\text{distance})^{-2}$
4. $(\text{velocity})^{\frac{2}{3}}$

Solution:

\text{Hint: The acceleration of the particle is } a = \frac{d^2x}{dt^2} \text{Step: Find the acceleration of the particle.} \text{Given, distance } x = (t + 5)^{-1} \text{ ...(i)} \text{Differentiating Eq. (i) w.r.t. t, we get} \frac{dx}{dt} = v = \frac{-1}{(t+5)^2} \text{ ...(ii)} \text{Again, differentiating Eq. (ii) w.r.t. t, we get} \frac{d^2x}{dt^2} = a = \frac{2}{(t+5)^3} \text{ ...(iii)} \text{Comparing Eqs. (ii) and (iii), we get} a \propto v^{\frac{3}{2}} \text{Hence, option (1) 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
}