Import Question JSON

Current Question (ID: 19141)

Question:

$\text{An insect is at the bottom of a hemispherical ditch of radius } 1 \text{ m.}$ $\text{It crawls up the ditch but starts slipping after it is at height } h \text{ from the bottom.}$ $\text{If the coefficient of friction between the ground and the insect is } 0.75, \text{ then } h \text{ is: } (g = 10 \text{ m/s}^2)$

Options:

1. $0.20 \text{ m}$
2. $0.60 \text{ m}$
3. $0.45 \text{ m}$
4. $0.80 \text{ m}$

Solution:

$\text{Hint: Balance tangential forces.}$ $\text{For balancing } mg \sin \theta = f$ $mg \sin \theta = \mu mg \cos \theta$ $\tan \theta = \mu$ $\tan \theta = \frac{3}{4}$ $h = R - R \cos \theta$ $= R - R \left( \frac{4}{5} \right) = \frac{R}{5}$ $h = \frac{R}{5} = 0.2 \text{ m}$

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
}