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Current Question (ID: 20046)

Question:

$\text{Two identical metallic spheres } A \text{ and } B \text{ when placed at a certain distance in the air repel each other with a force } F. \text{ Another identical uncharged sphere } C \text{ is first placed in contact with } A \text{ and then in contact with } B \text{ and finally placed at the midpoint between spheres } A \text{ and } B. \text{ The force experienced by sphere } C \text{ will be:}$

Options:

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

Solution:

$\text{Hint: } F = \frac{kq_1q_2}{r^2}$ $\text{Step 1: Find the magnitude of force } F.$ $F = \frac{kq^2}{r^2}$ $\text{Step 2: Find the new charges on spheres } A, B \text{ and } C.$ $q_A = \frac{q + 0}{2} = \frac{q}{2}$ $q_B = \frac{q/2 + q}{2} = \frac{3q}{4}$ $q_C = \frac{q/2 + q}{2} = \frac{3q}{4}$ $\text{Step: Find the force experienced by sphere } C.$ $F_C = F_B - F_A$ $\Rightarrow F_C = \frac{k(3q/4)(3q/4)}{(r/2)^2} - \frac{k(q/2)(3q/4)}{(r/2)^2}$ $\Rightarrow F_C = \frac{9kq^2}{4r^2} - \frac{6kq^2}{4r^2}$ $\Rightarrow F_C = \frac{3kq^2}{4r^2} = \frac{3F}{4}$ $\Rightarrow F_C = \frac{3F}{4}$ $\text{Hence, option (2) is the correct answer.}$

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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
}