Import Question JSON

Current Question (ID: 16475)

Question:

$\text{Three charges } Q, +q \text{ and } +q \text{ are placed at the vertices of an equilateral triangle of side } l \text{ as shown in the figure. If the net electrostatic energy of the system is zero, then } Q \text{ is equal to:}$

Options:

1. $-\frac{q}{2}$
2. $-q$
3. $+q$
4. $\text{zero}$

Solution:

$\text{Hint: } U = k \frac{q_1 q_2}{r}$ $\text{Step: Find the value of the charge } Q$ $\text{The potential energy of the system is given by:}$ $U = \frac{kQq}{l} + \frac{kq^2}{l} + \frac{kqQ}{l} = 0$ $\Rightarrow \frac{kq}{l} (Q + q + Q) = 0$ $\Rightarrow Q = -\frac{q}{2}$ $\text{Hence, option (1) is the correct answer.}$

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
}