Import Question JSON

Current Question (ID: 9618)

Question:

$\text{A body is projected with velocity } \vec{v} = (\alpha \hat{i} + \beta \hat{j}) \text{ m/s. The time of flight of the body is: [considering } x \text{ as horizontal and } y \text{ as vertical axis and } g \text{ is acceleration due to gravity]}$

Options:

1. $\frac{2\beta}{g}$
2. $\frac{2\alpha}{g}$
3. $\frac{2\alpha\beta}{g}$
4. $\frac{2\alpha}{g\beta}$

Solution:

\text{Hint: Time of flight is given as } T = \frac{2u_y}{g} \text{Step 1: Find the vertical component of the velocity.} \vec{u} = (\alpha \hat{i} + \beta \hat{j}) \text{ m/s} u_x = \alpha \text{ m/s} u_y = \beta \text{ m/s} \text{Step 2: Calculate the time of flight.} \text{Hence the time of the flight is:} T = \frac{2u_y}{g} = \frac{2\beta}{g} \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
}