Import Question JSON

Current Question (ID: 9542)

Question:

\text{Consider the motion of the tip of the second hand of a clock. In one minute (assuming } R \text{ to be the length of the second hand), its:}

Options:

1. $\text{displacement is } 2\pi R$
2. $\text{distance covered is } 2R$
3. $\text{displacement is zero.}$
4. $\text{distance covered is zero.}$

Solution:

$\text{Hint: Displacement} = x_f - x_i$ $\text{Explanation: In the context of the second hand of a clock, even though it moves in a circular path, when it completes one full revolution, it returns to its initial position. Hence, its displacement from the starting point to the ending point is indeed zero i.e., } x_f = x_i.$ $\text{Hence, option (3) is the correct answer.}$

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
}