Import Question JSON

Current Question (ID: 9603)

Question:

$\text{A frictionless wire } AB \text{ is fixed on a sphere of radius } R\text{. A very small spherical ball slips on this wire. The time taken by this ball to slip from } A \text{ to } B \text{ is:}$

Options:

1. $\frac{2\sqrt{gR}}{g\cos\theta}$
2. $2\sqrt{gR} \cdot \frac{\cos\theta}{g}$
3. $2\sqrt{\frac{R}{g}}$
4. $\frac{gR}{\sqrt{g\cos\theta}}$

Solution:

\text{Hint: } s = ut + \frac{1}{2}gt^2 \text{Step: Find the time taken by this ball to slip from } A \text{ to } B\text{.} \text{Acceleration of the body along } AB \text{ is } g\cos\theta \text{Distance travelled in time } t \text{ sec} = AB = \frac{1}{2}(g\cos\theta)t^2 \text{From triangle } ABC, AB = 2R\cos\theta; \quad 2R\cos\theta = \frac{1}{2}g\cos\theta t^2 \Rightarrow t^2 = \frac{4R}{g} \text{ or } t = 2\sqrt{\frac{R}{g}} \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
}