Import Question JSON

Current Question (ID: 20194)

Question:

$64$ $\text{identical balls made of conducting material with a potential of } 10 \text{ mV are joined to form a bigger ball. The potential of the bigger ball is:}$

Options:

1. $150 \text{ mV}$
2. $160 \text{ mV}$
3. $120 \text{ mV}$
4. $100 \text{ mV}$

Solution:

$\text{Hint: } V = \frac{kQ}{R}$ $\text{Explanation: let the radius of smaller and bigger ball is } r \text{ and } R \text{ respectively.}$ $\text{Let the mass of the smaller and bigger ball is } m \text{ and } M \text{ respectively.}$ $M = 64 \, m \Rightarrow \frac{4\pi R^3}{3} \rho = 64 \frac{4\pi r^3}{3} \rho$ $64(\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3 \Rightarrow R = 4r \quad (1)$ $\text{Let the charge of the smaller and bigger ball is } q \text{ and } Q \text{ respectively.}$ $Q = 64 \, q \quad (2)$ $\text{The potential of a bigger ball is given by using the (1) and (2) equations.}$ $V = \frac{KQ}{R} = \frac{K(64q)}{4r} = 16 \frac{Kq}{r} = 16 \times 10 \text{ mV} = 160 \text{ mV}$ $\text{Option (2) is correct.}$

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
}