Import Question JSON

Current Question (ID: 19097)

Question:

$\text{A projectile is launched from a horizontal surface with an initial velocity } u. \text{ At its maximum height, the velocity of the projectile is } \frac{\sqrt{3}u}{2}. \text{ The time of flight of the projectile is:}$

Options:

1. $\frac{\sqrt{3}u}{g}$
2. $\frac{2u}{g}$
3. $\frac{u}{g}$
4. $\frac{u}{2g}$

Solution:

$\text{Hint: } x\text{-component of velocity remains constant throughout the motion.}$ $\text{Step 1: Find the angle of projection, } \theta.$ $\text{The velocity of the ball at maximum height is given by:}$ $u \cos \theta = \frac{\sqrt{3}u}{2}$ $\Rightarrow \cos \theta = \frac{\sqrt{3}}{2}$ $\Rightarrow \theta = 30^\circ$ $\text{Step 2: Find the time of flight of the projectile.}$ $\text{The time of flight of the projectile is given by:}$ $T = \frac{2u \sin \theta}{g}$ $\Rightarrow T = \frac{2u \sin 30^\circ}{g}$ $\Rightarrow T = \frac{u}{g}$ $\text{Hence, option (3) is the correct answer.}$

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
}