Import Question JSON

Current Question (ID: 19540)

Question:

$\text{The elongation of a wire on the surface of the Earth is } 10^{-4} \text{ m. The same wire, of the same dimensions, elongates by } 6 \times 10^{-5} \text{ m on another planet. The acceleration due to gravity on the planet will be:}$ $\text{(take acceleration due to gravity on the surface of the Earth as } 10 \text{ m s}^{-2})$

Options:

1. $5 \text{ ms}^{-2}$
2. $6 \text{ ms}^{-2}$
3. $7 \text{ ms}^{-2}$
4. $8 \text{ ms}^{-2}$

Solution:

$\text{Hint: } \Delta L \propto g$ $\text{Step: Find the acceleration due to gravity on the planet.}$ $\text{The elongation of a wire is given by:}$ $\Delta L = \frac{FL}{AY} = \frac{mgL}{AY}$ $\Rightarrow \Delta L \propto g$ $\Rightarrow \frac{\Delta L_1}{\Delta L_2} = \frac{g_1}{g_2}$ $\Rightarrow g_2 = g_1 \left( \frac{\Delta L_2}{\Delta L_1} \right)$ $\Rightarrow g_2 = g \left( \frac{\Delta L_2}{\Delta L_1} \right) = \frac{10 \times 6 \times 10^{-5}}{10^{-4}}$ $\Rightarrow g_2 = 6 \text{ ms}^{-2}$ $\text{Hence, option (2) is the correct answer.}$

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
}