Import Question JSON

Current Question (ID: 19548)

Question:

$\text{Wire } A \text{ and } B \text{ have their Young's moduli in the ratio } 1:3 \text{, area of the cross-section in the ratio of } 1:2 \text{ and lengths in the ratio of } 3:4. \text{ If the same force is applied on the two wires to elongate then the ratio of elongation is equal to:}$ $1.\ 8:1$ $2.\ 1:12$ $3.\ 1:8$ $4.\ 9:2$

Options:

1. $8:1$
2. $1:12$
3. $1:8$
4. $9:2$

Solution:

$\text{Hint: } Y = \frac{F/A}{\Delta l/l} \Rightarrow \frac{Fl}{\Delta l A}$ $\text{Step: Find the ratio of elongation on the two wires.}$ $\text{The Young's modulus of the wire is given by:}$ $Y = \frac{Fl}{\Delta l A}$ $\text{As force is applied on both wires are same, so } \Delta l \propto \frac{l}{YA}$ $\Delta l_a = \frac{l_a}{A_a Y_a}, \Delta l_b = \frac{l_b}{A_b Y_b}$ $\text{The ratio of the elongation will be:}$ $\frac{\Delta l_A}{\Delta l_B} = \frac{l_A}{l_B} \times \frac{A_B}{A_A} \times \frac{Y_B}{Y_A}$ $\Rightarrow \frac{\Delta l_A}{\Delta l_B} = \frac{3}{4} \times \frac{2}{1} \times \frac{3}{1}$ $\Rightarrow \frac{\Delta l_A}{\Delta l_B} = \frac{9}{2}$ $\text{Hence, option (4) is the correct answer.}$

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
}