Import Question JSON

Current Question (ID: 8879)

Question:

$\text{A particle is allowed to fall from rest from a height } h\text{. Which of the following represents its velocity versus time graph?}$

Options:

1. $\text{Graph showing a horizontal line at constant velocity } \sqrt{2gh}$
2. $\text{Graph showing a straight line with positive slope starting from origin, reaching } \sqrt{2gh} \text{ at time } \sqrt{\frac{2h}{g}}$
3. $\text{Graph showing a curved line that increases at a decreasing rate, reaching } \sqrt{2gh} \text{ at time } \sqrt{\frac{2h}{g}}$
4. $\text{Graph showing a curved line that increases at an increasing rate, reaching } \sqrt{2gh} \text{ at time } \sqrt{\frac{2h}{g}}$

Solution:

$\text{Hint: } v = \sqrt{2gh}$ $\text{Step: Find the correct velocity versus time graph.}$ $\text{For a free-falling body,}$ $v \propto t \Rightarrow \text{ the v-graph is a straight line.}$ $\text{(Take the downward direction as the positive direction.)}$ $\text{Therefore, option (2) represents the correct velocity versus time graph.}$ $\text{Hence, option (2) is the correct answer.}$

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
}