Import Question JSON

Current Question (ID: 10480)

Question:

$\text{A sniper fires a rifle bullet into a gasoline tank making a hole 53.0 m below the surface of gasoline. The tank was sealed at 3.10 atm. The stored gasoline has a density of 660 kgm}^{-3}\text{. The velocity with which gasoline begins to shoot out of the hole will be:}$

Options:

1. $27.8 \text{ ms}^{-1}$
2. $41.0 \text{ ms}^{-1}$
3. $9.6 \text{ ms}^{-1}$
4. $19.7 \text{ ms}^{-1}$

Solution:

$\text{According to Bernoulli's theorem:}$ $P_B + h\rho g = P_A + \frac{1}{2}\rho v_A^2 \quad (\text{As } v_A >> v_B)$ $\text{Substituting the given values:}$ $3.10P + 53 \times 660 \times 10 = P + \frac{1}{2} \times v_A^2$ $\Rightarrow 2.1 \times 1.01 \times 10^5 + 3.498 \times 10^5 = \frac{1}{2} \times 660 \times v_A^2$ $\Rightarrow 5.619 \times 10^5 = \frac{1}{2} \times 660 \times v_A^2$ $\therefore v_A = \sqrt{\frac{2 \times 5.619 \times 10^5}{660}} = 41 \text{ m/s}$

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
}