Import Question JSON

Current Question (ID: 10237)

Question:

$\text{A man 'A', mass 60 kg, and another man 'B', mass 70 kg, are sitting at the two extremes of a 2 m long boat, of mass 70 kg, standing still in the water as shown. They come to the middle of the boat. (Neglect friction) How far does the boat move on the water during the process?}$

Options:

1. $\text{5 cm leftward}$
2. $\text{5 cm rightward}$
3. $\text{7 cm leftward}$
4. $\text{7 cm rightward}$

Solution:

$\text{Hint: There is no external force on the system so the position of the centre of mass will remains the same.}$ $\text{Step 1: Draw the diagram.}$ $\text{The diagram shows a boat with two people A and B at the extremes, with positive direction indicated and } V_{CM} = 0$ $\text{Step 2:}$ $\text{If } F_{ext} = 0$ $\Rightarrow \sum \Delta m_i \vec{x}_i = 0$ $\Rightarrow 70x + 60(x + 1) + 70(x - 1) = 0$ $\Rightarrow x = 5 \text{ cm}$

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
}