Import Question JSON

Current Question (ID: 19094)

Question:

$\text{An object is projected in the air with initial velocity } u \text{ at an angle } \theta. \text{ The projectile motion is such that the horizontal range } R, \text{ is maximum. Another object is projected in the air with a horizontal range half of the range of the first object. The initial velocity remains the same in both cases. The value of the angle of projection, at which the second object is projected, will be:}$

Options:

1. $45^\circ$
2. $30^\circ$
3. $60^\circ$
4. $15^\circ$

Solution:

$\text{Hint: } R = \frac{u^2 \sin 2\theta}{g}$ $\text{Step: Find the angle of projection (} \theta \text{) of second projectile.}$ $\text{The first projectile is projected at } 45^\circ, \text{ that means it covers maximum range.}$ $\text{Then, } R_1 = \frac{u^2}{g}$ $\text{For, second projectile; } R_2 = \frac{u^2 \sin 2\theta}{g}$ $\text{Also, according to question; } R_1 = 2R_2$ $\text{Therefore, } \frac{1}{2} \frac{u^2}{g} = \frac{u^2 \sin 2\theta}{g}$ $\Rightarrow \theta = 15^\circ$ $\text{Hence, option (4) is the correct answer.}$

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
}