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Current Question (ID: 16408)

Question:

$\text{Two spherical conductors } B \text{ and } C \text{ having equal radii and carrying equal charges in them repel each other with a force } F \text{ when kept apart at some distance. A third spherical conductor having same radius as that of } B \text{ but uncharged is brought in contact with } B, \text{ then brought in contact with } C \text{ and finally removed away from both. The new force of repulsion between } B \text{ and } C \text{ is:}$

Options:

1. $\frac{F}{4}$
2. $\frac{3F}{4}$
3. $\frac{F}{8}$
4. $\frac{3F}{8}$

Solution:

$\text{Hint - Conductors in contact have same potential}$ $\text{Step 1}$ $\text{Find the force B and C, when there is no other conductor.}$ $\text{Initially } F = k \cdot \frac{Q^2}{r^2} \text{ (fig. A).}$ $\text{Step 2}$ $\text{Find the force B and C, when another conductor comes in contact with B and C.}$ $\text{Finally, when a third spherical conductor comes in contact alternately with B and C then removed, so charges on B and C are } Q/2 \text{ and } 3Q/4 \text{ respectively (fig. B).}$ $\text{Now force } F' = k \cdot \left(\frac{Q}{2}\right) \left(\frac{3Q}{4}\right) \frac{1}{r^2} = \frac{3}{8}F$

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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
}