Import Question JSON

Current Question (ID: 10366)

Question:

The Young's modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of:

Options:

1. $1:2$
2. $2:1$
3. $4:1$
4. $1:1$

Solution:

\text{Given: } Y_{\text{steel}} = 2Y_{\text{brass}} \text{ and } L_s = L_b \text{ and } A_s = A_b \text{such that } \Delta L_s = \Delta L_b \text{As we know, Young's modulus} Y = \frac{\text{stress}}{\text{strain}} = \frac{W/A}{\Delta L/L} \text{i.e. } \frac{W_s}{W_b} = \frac{Y_s}{Y_b} = \frac{2Y_b}{Y_b} = \frac{2}{1} \therefore \text{ ratio is } 2:1 \text{Thus, weight added to the steel and brass wires must be in the ratio of } 2:1

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
}