Import Question JSON

Current Question (ID: 19308)

Question:

$\text{In a simple pendulum of length } 10 \text{ m, the string is initially kept horizontal and the bob is released. } 10\% \text{ of energy is lost till the bob reaches the lowermost position. Then find the speed of the bob at the lowermost position.}$

Options:

1. $6 \text{ m/s}$
2. $6\sqrt{5} \text{ m/s}$
3. $7\sqrt{5} \text{ m/s}$
4. $4\sqrt{2} \text{ m/s}$

Solution:

$\text{Hint: Apply the conservation of energy.}$ $W_{\text{total}} = \Delta K$ $\Rightarrow \ 0.9 \ mgl = \frac{1}{2} mv^2$ $\Rightarrow \ v = \sqrt{1.8 \times 10 \times 10}$ $= 6\sqrt{5} \text{ m/s}$

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
}