Import Question JSON

Current Question (ID: 20036)

Question:

$\text{Two small spheres each of mass } 10 \text{ mg are suspended from a point by threads } 0.5 \text{ m long.}$ $\text{They are equally charged and repel each other to a distance of } 0.20 \text{ m.}$ $\text{The charge on each of the spheres is } \frac{a}{21} \times 10^{-8} \text{ C.}$ $\text{The value of } 'a' \text{ will be:}$ $\text{(given } g = 10 \text{ ms}^{-2})$

Options:

1. $25$
2. $30$
3. $40$
4. $20$

Solution:

$\text{Balance the forces in horizontal and vertical directions.}$ $\text{Find the value of } a.$ $T \cos \theta = mg = 10 \times 10^{-6} \times 10 = 10^{-4}$ $T \sin \theta = \frac{9 \times 10^9 \cdot q^2}{0.04} = F$ $\tan \theta = \frac{0.1}{\sqrt{0.24}} = \frac{F}{mg} = \frac{1}{5}$ $mg = 5F$ $10 \times 10^{-6} \times 10 = \frac{5 \times 9 \times 10^9 \cdot q^2}{(0.2)^2}$ $a^2 \approx 400 \Rightarrow a = 20$ $\text{Hence, option (4) is the correct answer.}$

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
}