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Current Question (ID: 16391)

Question:

$\text{A total charge } Q \text{ is broken in two parts } Q_1 \text{ and } Q_2 \text{ and they are placed at a distance } R \text{ from each other. The maximum force of repulsion between them will occur, when:}$

Options:

1. $Q_2 = \frac{Q}{R}, Q_1 = Q - \frac{Q}{R}$
2. $Q_2 = \frac{Q}{4}, Q_1 = Q - \frac{2Q}{3}$
3. $Q_2 = \frac{Q}{4}, Q_1 = \frac{3Q}{4}$
4. $Q_1 = \frac{Q}{2}, Q_2 = \frac{Q}{2}$

Solution:

$\text{(4) } Q_1 + Q_2 = Q \quad \text{(i) and } F = \frac{kQ_1Q_2}{r^2} \quad \text{(ii)}$ $\text{From (i) and (ii), } F = \frac{kQ_1(Q-Q_1)}{r^2}$ $\text{For } F \text{ to be maximum: } \frac{dF}{dQ_1} = 0 \Rightarrow Q_1 = Q_2 = \frac{Q}{2}$

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
}