Import Question JSON

Current Question (ID: 8884)

Question:

$\text{A falling stone from rest takes 0.2 s to fall past a window on path which is 1 m high. From how far above the top of window, was the stone dropped?}$

Options:

1. $\frac{4}{5} \text{ m}$
2. $\frac{5}{7} \text{ m}$
3. $\frac{9}{5} \text{ m}$
4. $\frac{5}{9} \text{ m}$

Solution:

$\text{Hint: } s = ut - \frac{1}{2}gt^2$ $\text{Step 1}$ $s = ut - \frac{1}{2}gt^2$ $h = 0 - \frac{1}{2}gt^2 \quad [u = 0]$ $h = \frac{1}{2}gt^2 \quad \ldots (1)$ $h + 1 = \frac{1}{2}g(t)^2 \quad \ldots (2)$ $h = \frac{1}{2}g(t - 0.2)^2 \quad \ldots (3)$ $\text{From (2) and (3) we get,}$ $\sqrt{\frac{h + 1}{5}} = t \quad \ldots (4)$ $\sqrt{\frac{h}{5}} = t - 0.2 \quad \ldots (5)$ $\Rightarrow \text{Subtracting (4) from (5) we get,}$ $\sqrt{\frac{h+1}{5}} - \sqrt{\frac{h}{5}} = 0.2 \quad \ldots (6)$ $\text{Now solve the equation using } h = \frac{4}{5} \text{m.}$ $\sqrt{\frac{9}{5 \times 5}} - \sqrt{\frac{4}{5 \times 5}} = 0.2$ $\frac{3}{5} - \frac{2}{5} = 0.2$ $\frac{1}{5} = 0.2$ $\text{LHS = RHS}$ $\text{Hence, option (1) is the correct answer.}$

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
}