Import Question JSON

Current Question (ID: 8932)

Question:

$\text{A stone is dropped from a height } h\text{. Simultaneously, another stone is thrown up from the ground which reaches a height } 4h\text{. The two stones cross each other after time:}$

Options:

1. $\sqrt{\frac{h}{8g}}$
2. $\sqrt{8gh}$
3. $\sqrt{2gh}$
4. $\sqrt{\frac{h}{2g}}$

Solution:

$\text{Hint: } s = ut + \frac{1}{2}at^2$ $\text{Step: Find the time when two stones cross each other.}$ $\text{For the first stone } u = 0 \text{ and}$ $\text{For the second stone } \frac{u^2}{2g} = 4h \Rightarrow u^2 = 8gh$ $\therefore u = \sqrt{8gh}$ $\text{Now, } h_1 = \frac{1}{2}gt^2$ $h_2 = \sqrt{8gh}t - \frac{1}{2}gt^2$ $\text{where, } t = \text{time to cross each other.}$ $\therefore h_1 + h_2 = h$ $\Rightarrow \frac{1}{2}gt^2 + \sqrt{8gh}t - \frac{1}{2}gt^2 = h$ $\Rightarrow t = \frac{h}{\sqrt{8gh}} = \sqrt{\frac{h}{8g}}$ $\text{Hence, option (1) is the correct answer.}$

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
}