Import Question JSON

Current Question (ID: 9626)

Question:

$\text{Four bodies } P, Q, R \text{ and } S \text{ are projected with equal velocities having angles of projection } 15°, 30°, 45°, \text{ and } 60° \text{ with the horizontal respectively. The body having the shortest range is?}$

Options:

1. $P$
2. $Q$
3. $R$
4. $S$

Solution:

$\text{Hint: } R = \frac{u^2 \sin 2\theta}{g}$ $\text{Step: Find the body having the shortest range.}$ $\text{The range of the projectile is given by;}$ $R = \frac{u^2 \sin 2\theta}{g}$ $\text{The range of the projectile is maximum at the angle } 45°.$ $\text{When the angle of projection is very far from } 45° \text{ then the range will be minimum.}$ $\text{Therefore, the body } P \text{ has the shortest range.}$ $\text{Hence, option (1) is the correct answer.}$

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
}