Import Question JSON

Current Question (ID: 20246)

Question:

$\text{A wire with a resistance of } 5 \, \Omega \text{ is stretched (redrawn) to increase its length 5 times. What will be the final resistance of the wire?}$

Options:

1. $25 \, \Omega$
2. $16 \, \Omega$
3. $125 \, \Omega$
4. $32 \, \Omega$

Solution:

$\text{Hint: } R = \rho \frac{l}{A}$ $\text{Step: Find the final resistance of the wire.}$ $\Rightarrow R = \rho \frac{l}{A} = 5 \, \Omega$ $\text{The volume of wire is constant in stretching, so volume is constant.}$ $\Rightarrow l_0 A_0 = 5l_0 A$ $\Rightarrow A = \frac{A_0}{5}$ $R' = \rho \frac{l_0}{A/5} = \frac{25 \rho l_0}{A_0} = 25R = 125 \, \Omega$ $\text{Hence, option (3) is the correct answer.}$

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
}