Import Question JSON

Current Question (ID: 10235)

Question:

$\text{A man hangs from a rope attached to a hot-air balloon. The man's mass is greater than the mass of the balloon and its contents. The system is stationary in the air. If the man now climbs up the balloon using the rope, the centre of mass of the 'man plus balloon' system will:}$

Options:

1. $\text{remain stationary}$
2. $\text{move up}$
3. $\text{move down}$
4. $\text{first moves up and then return to its initial position}$

Solution:

$\text{Hint: Movement of the centre of mass depends only on the external force.}$ $\text{Step 1: Draw the FBD}$ $\text{The diagram shows a stationary system with a balloon and man, where the center of mass (CM) is marked, with buoyant force } F_B \text{ upward and weight } W \text{ downward.}$ $\text{Step 2: Calculate net external force.}$ $\text{Here the weight of the centre of mass is balanced by the buoyant force.}$ $\text{So, the net force on the system is zero.}$ $\text{Hence centre of mass will remains the same.}$

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
}