Import Question JSON

Current Question (ID: 9884)

Question:

$\text{A ball is dropped from a height of 5 m. If it rebounds up to a height of 1.8 m, then the ratio of velocities of the ball after and before the rebound will be:}$

Options:

1. $\frac{3}{5}$
2. $\frac{2}{5}$
3. $\frac{1}{5}$
4. $\frac{4}{5}$

Solution:

$\text{When the ball is dropped from 5 m height:}$ $v_1 = \sqrt{2g \times 5}$ $\text{When the ball rebounds to 1.8 m height:}$ $v_2 = \sqrt{2g \times 1.8}$ $\text{The ratio of velocities after and before rebound:}$ $\frac{v_2}{v_1} = \frac{\sqrt{2g \times 1.8}}{\sqrt{2g \times 5}} = \sqrt{\frac{1.8}{5}} = \sqrt{\frac{18}{50}} = \sqrt{\frac{9}{25}} = \frac{3}{5}$

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
}