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Current Question (ID: 16496)

Question:

$\text{Two metallic spheres of radii 1 cm and 3 cm are given charges of}$ $-1 \times 10^{-2} \text{ C and } 5 \times 10^{-2} \text{ C, respectively.}$ $\text{If these are connected by a conducting wire, the final charge on the bigger sphere is:}$

Options:

1. $2 \times 10^{-2} \text{ C}$
2. $3 \times 10^{-2} \text{ C}$
3. $4 \times 10^{-2} \text{ C}$
4. $1 \times 10^{-2} \text{ C}$

Solution:

$\text{The charge will flow from high potential to low potential until the electric}$ $\text{potential is same for both the spheres.}$ $\text{If } Q_1 \text{ and } Q_2 \text{ are the final charges on the spheres,}$ $\frac{KQ_1}{3} = \frac{KQ_2}{1}$ $Q_1 = 3Q_2$ $\text{Also, by the conservation of charges,}$ $Q_1 + Q_2 = 4 \times 10^{-2}$ $4Q_2 = 4 \times 10^{-2}$ $Q_2 = 10^{-2}$ $\text{and}$ $Q_1 = 3 \times 10^{-2} \text{ C}$

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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
}