Import Question JSON

Current Question (ID: 19151)

Question:

$\text{A hanging mass } M \text{ is connected to four times bigger mass by using a string-pulley arrangement as shown in the figure.}$ $\text{The bigger mass is placed on a horizontal ice slab and pulled by } 2 \ Mg \text{ force.}$ $\text{In this situation, tension in the string is } \frac{x}{5} Mg \text{ for the value of } x:$ $\text{(Neglect the mass of the string and friction of the block (bigger mass) with ice slab.)}$ $\text{(Given } g = \text{ acceleration due to gravity)}$

Options:

1. 6
2. 3
3. 9
4. 2

Solution:

$\text{Using } \vec{F}_{\text{net}} = \mu \vec{a}$ $2Mg - T = 4Ma$ $T - Mg = Ma$ $T = Mg + Ma = Mg + \frac{Mg}{5} = \frac{6}{5} Mg$ $\Rightarrow a = \frac{g}{5}$

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
}