Import Question JSON

Current Question (ID: 19555)

Question:

$\text{A wire of natural length } L \text{ is suspended vertically from a fixed point.}$ $\text{The length changes to } L_1 \text{ and } L_2 \text{ when masses 1 kg and 2 kg are}$ $\text{suspended, respectively, from its free end. The value of } L \text{ is:}$

Options:

1. $\sqrt{L_1 L_2}$
2. $\frac{L_1 + L_2}{2}$
3. $2L_1 - L_2$
4. $3L_1 - 2L_2$

Solution:

$\text{Hint: } Y = \frac{FL}{A \Delta L}$ $\text{Step: Find the initial length of the hanging wire.}$ $\text{By applying the hooks law;} \ F \propto \Delta L$ $\Rightarrow \frac{F_1}{F_2} = \frac{\Delta L_1}{\Delta L_2}$ $\Rightarrow \frac{10}{20} = \frac{L_1 - L}{L_2 - L}$ $\Rightarrow L = 2L_1 - L_2$ $\text{Hence, option (3) is the correct answer.}$

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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
}