Import Question JSON

Current Question (ID: 9636)

Question:

$\text{A projectile is projected with initial kinetic energy }K\text{. If it has kinetic energy }0.25K\text{ at its highest point, then the angle of projection is:}$

Options:

1. $30°$
2. $45°$
3. $60°$
4. $75°$

Solution:

\text{Hint: At the highest point; } v_y = 0 \text{Step: Find the angle of the projectile.} \text{If the initial velocity of the particle is } u\text{,} \text{The initial kinetic energy, } K = \frac{1}{2}mu^2 \text{At the highest point, } K' = \frac{1}{2}mu^2 \cos^2 \theta \text{As, } K' = 0.25K\text{,} \Rightarrow \frac{1}{2}mu^2 \cos^2 \theta = \frac{1}{2}mu^2 \times 0.25 \Rightarrow \cos^2 \theta = 0.25 \Rightarrow \cos \theta = 0.5 = \frac{1}{2} = \cos 60° \Rightarrow \theta = 60° \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
}