Import Question JSON

Current Question (ID: 19095)

Question:

$\text{If a ball is thrown from the ground in a vertical plane and reaches a maximum height of } 360 \text{ m, the maximum horizontal distance it can cover on level ground using the same launch speed is:}$

Options:

1. $360 \text{ m}$
2. $720 \text{ m}$
3. $1440 \text{ m}$
4. $180 \text{ m}$

Solution:

$\text{Hint: For maximum horizontal range, the projection angle should be } 45^\circ.$ $\text{Step: Find the maximum distance, the ball can cover on ground keeping the projection speed constant.}$ $\text{The maximum height of the projectile is given by:}$ $H_{\text{max}} = \frac{u^2}{2g}$ $\Rightarrow \frac{u^2}{g} = 2H_{\text{max}}$ $\Rightarrow \frac{u^2}{g} = 2 \times 360$ $\Rightarrow R_{\text{max}} = 720 \text{ m} \quad \left[\therefore R_{\text{max}} = \frac{u^2}{g}\right]$ $\text{Hence, option (2) is the correct answer.}$

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
}