Import Question JSON

Current Question (ID: 8928)

Question:

$\text{A boy falls from a building of height 320 m. After 5 seconds, superman jumps downward with initial speed } u \text{ such that the boy can be saved. The minimum value of } u \text{ is: (assume } g = 10 \text{ m/s}^2\text{)}$

Options:

1. $95.1 \text{ m/s}$
2. $98.3 \text{ m/s}$
3. $91.6 \text{ m/s}$
4. $85.6 \text{ m/s}$

Solution:

$\text{Hint: Use the second equation of motion}$ $\text{Step 1: Find the position of the boy after 5 sec}$ $S = \frac{1}{2}at^2$ $= \frac{1}{2} \times 10 \times 5^2$ $= 125 \text{ m}$ $v = u + at$ $v = 0 + 10 \times 5$ $= 50 \text{ m/s}$ $\text{Step 2: Use the concept of relative motion.}$ $a_{S,B} = g - g = 0$ $u_{S,B} = u - 50$ $S_{S,B} = 125$ $\text{Step 3: Find the time of flight of the boy}$ $t = \sqrt{\frac{2h}{g}} = 8 \text{ s}$ $3(u - 50) = 125$ $u \approx 91.6 \text{ m/s}$ $\text{Hence, option (3) is the correct answer.}$

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
}