Import Question JSON

Current Question (ID: 10342)

Question:

$\text{A light rod of length 2 m is suspended from the ceiling horizontally by means of two vertical wires of equal length. A weight } W \text{ is hung from the light rod as shown in the figure. The rod is hung by means of a steel wire of cross-sectional area } A_1 = 0.1 \text{ cm}^2 \text{ and brass wire of cross-sectional area } A_2 = 0.2 \text{ cm}^2\text{. To have equal stress in both wires, } \frac{T_1}{T_2} \text{?}$

Options:

1. $\frac{1}{3}$
2. $\frac{1}{4}$
3. $\frac{4}{3}$
4. $\frac{1}{2}$

Solution:

\text{To have equal stress produced in the wires:} \text{Stress is defined as } \sigma = \frac{F}{A} = \frac{T}{A} \text{For equal stress in both wires:} \frac{T_1}{A_1} = \frac{T_2}{A_2} \text{Rearranging:} \frac{T_1}{T_2} = \frac{A_1}{A_2} \text{Substituting the given values:} \frac{T_1}{T_2} = \frac{0.1}{0.2} = \frac{1}{2} \text{Therefore: } \frac{T_1}{T_2} = \frac{1}{2}

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
}