Import Question JSON

Current Question (ID: 16404)

Question:

$\text{Three charges are placed at the vertices of an equilateral triangle of side } a \text{ as shown in the following figure. The force experienced by the charge placed at the vertex } A \text{ in a direction normal to } BC \text{ is:}$

Options:

1. $\frac{Q^2}{4 \pi \epsilon_0 a^2}$
2. $-\frac{Q^2}{4 \pi \epsilon_0 a^2}$
3. $\text{zero}$
4. $\frac{Q^2}{2 \pi \epsilon_0 a^2}$

Solution:

$\text{Hint: } F = \frac{k q_1 q_2}{r^2}$ $\text{Step 1: Find the forces acting on charge at } A \text{ due to charges at } B \text{ and } C.$ $|\vec{F}_B| = |\vec{F}_C| = k \times \frac{Q^2}{a^2}$ $\text{Step 2: Draw the components of forces to find the resultant force experienced by the charge at } A.$ $\text{Thus the force experienced by the charge at } A \text{ in the direction normal to } BC \text{ is zero.}$ $\text{Hence, option (3) is the correct answer.}$

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
}