Import Question JSON

Current Question (ID: 10116)

Question:

$\text{A boat of length 10 m and a mass of 450 kg is floating without motion in still water. A man of 50 kg standing at one end walks to the other end and comes to a stop. The magnitude of the displacement of the boat relative to the ground is:}$

Options:

1. $\text{zero}$
2. $\text{1 m}$
3. $\text{2 m}$
4. $\text{5 m}$

Solution:

$\text{Let } m = \text{mass of man, } M = \text{mass of boat}$ $\text{Then, } m = 50 \text{ kg, } M = 450 \text{ kg}$ $\text{Let } x = \text{displacement of man w.r.t ground}$ $X = \text{displacement of boat w.r.t ground}$ $\text{Then, } x + X = L \text{ and } mx = MX$ $\Rightarrow x + X = 10 \text{ and } 50x = 450X$ $\text{On solving, we get } X = 1 \text{ m}$

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
}