Import Question JSON

Current Question (ID: 19336)

Question:

$\text{In the figure, there's a rigid and uniform rod } AB, \text{ one meter long, held horizontally by two strings tied to its ends and attached to the ceiling.}$ $\text{The rod has a mass of } m \text{ and another weight of the mass } 2m \text{ is hung at a distance of } 75 \text{ cm from } A. \text{ The tension in the string at the point } A \text{ is:}$

Options:

1. $2mg$
2. $0.5mg$
3. $0.75mg$
4. $mg$

Solution:

$\text{The system is in rotational and translational equilibrium.}$ $\text{Therefore, the net torque about point } B \text{ is zero.}$ $\left(T_A\right) \times 100 - mg \times 50 - (2mg) \times 25 = 0$ $\Rightarrow 100T_A = 100mg$ $\Rightarrow T_A = mg$ $\text{Hence, option (4) is the correct answer.}$

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
}