Import Question JSON

Current Question (ID: 19575)

Question:

$\text{A air bubble of radius } 1 \text{ cm in water has an upward acceleration } 9.8 \text{ cm/s}^2. \text{ The density of water is } 1 \text{ gm/cm}^3 \text{ and water offers negligible drag force on the bubble. The mass of the bubble is: } (g = 980 \text{ cm/s}^2)$

Options:

1. $3.15 \text{ gm}$
2. $1.52 \text{ gm}$
3. $4.51 \text{ gm}$
4. $4.15 \text{ gm}$

Solution:

$\text{Volume } \quad V = \frac{4\pi}{3} r^3 = \frac{4\pi}{3} \times (1)^3 = 4.19 \text{ cm}^3$ $a = 9.8 \text{ cm/s}^2$ $B - mg = ma$ $m = \frac{B}{g+a}$ $m = \frac{(V \rho_w g)}{g+a} = \frac{V \rho_w}{1+\frac{a}{g}}$ $= \frac{(4.19) \times 1}{1+\frac{9.8}{980}} = \frac{4.19}{1.01} = 4.15 \text{ gm}$

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
}