Import Question JSON

Current Question (ID: 8853)

Question:

$\text{A boy standing at the top of a tower of 20 m height drops a stone. Assuming } g = 10 \text{ m/s}^2\text{, the velocity with which it hits the ground will be:}$

Options:

1. $20 \text{ m/s}$
2. $40 \text{ m/s}$
3. $5 \text{ m/s}$
4. $10 \text{ m/s}$

Solution:

$\text{Hint: } v^2 - u^2 = 2as$ $\text{Step: Find the final velocity of the stone.}$ $\text{According to the third equation of motion we have:}$ $v^2 - u^2 = 2as$ $\Rightarrow v^2 = 2gh \quad [u = 0, s = h]$ $\Rightarrow v = \sqrt{2gh}$ $\Rightarrow v = \sqrt{2 \times 10 \times 20} = 20 \text{ m/s}$ $\text{Hence, option (1) is the correct answer.}$

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
}