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Current Question (ID: 20098)

Question:

$\text{Two identical conducting spheres } P \text{ and } S \text{ with charge } Q \text{ on each, repel each other with a force } 16 \text{ N.}$ $\text{A third identical uncharged conducting sphere } R \text{ is successively brought in contact with the two spheres.}$ $\text{The new force of repulsion between } P \text{ and } S \text{ is:}$

Options:

1. $4 \text{ N}$
2. $1 \text{ N}$
3. $6 \text{ N}$
4. $12 \text{ N}$

Solution:

$\text{Initially, the force between } P \text{ and } S \text{ is } F = \frac{kQ^2}{r^2} = 16 \text{ N.}$ $\text{When sphere } R \text{ is brought in contact with } P, \text{ the charge on each becomes } \frac{Q}{2}. \text{ Similarly, after contact with } S, \text{ the charge on each becomes } \frac{Q}{2}. \text{ The new force is } F' = \frac{k(\frac{Q}{2})^2}{r^2} = \frac{16}{4} = 4 \text{ N.}$

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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
}