Import Question JSON

Current Question (ID: 19403)

Question:

$\text{A particle of mass } m \text{ is projected with speed } v \text{ at an angle of } 30^\circ \text{ with the horizontal.}$ $\text{When the particle is at the maximum height, its angular momentum about the point of projection is:}$

Options:

1. $\frac{mv^3}{16g}$
2. $\frac{\sqrt{3}mv^3}{16g}$
3. $\frac{mv^3}{3g}$
4. $\frac{\sqrt{3}mv^3}{8g}$

Solution:

$\text{Hint: } L = mvr$ $\text{Step: Find the angular momentum of the particle about the point of projection.}$ $L = mvr$ $\Rightarrow L = m \times (v \cos 30^\circ) \times \frac{v^2 \sin^2 30^\circ}{2g}$ $\Rightarrow L = m \times \frac{v \sqrt{3}}{2} \times \frac{v^2}{8g}$ $\Rightarrow L = \frac{\sqrt{3}mv^3}{16g}$ $\text{Hence, option (2) is the correct answer.}$

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
}