Import Question JSON

Current Question (ID: 16620)

Question:

$\text{Two solid conductors are made up of the same material and have the same length and the same resistance.}$ $\text{One of them has a circular cross-section of area } A_1 \text{ and the other one has a square cross-section of area } A_2.}$ $\text{The ratio of } A_1/A_2 \text{ is:}$

Options:

1. $1.5$
2. $1$
3. $0.8$
4. $2$

Solution:

$\text{Hint: The resistance of a wire depends on the dimensions of the wire.}$ $\text{Step: Find the ratio of areas of the cross-section.}$ $\text{Since the resistances of the two conductors are the same;} \Rightarrow R_1 = R_2$ $\text{The formula of resistance is given by;} R = \rho \times \frac{l}{A}$ $\text{The ratio of areas of the cross-section } A_1/A_2 \text{ is given by;} \Rightarrow \rho \frac{l}{A_1} = \rho \frac{l}{A_2} \Rightarrow \frac{A_1}{A_2} = 1$ $\text{Hence, option (2) is the correct answer.}$

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
}