Import Question JSON

Current Question (ID: 16789)

Question:

$\text{A metallic rod of mass per unit length of } 0.5 \text{ kgm}^{-1} \text{ is lying horizontally on a smooth inclined plane which makes an angle of } 30^\circ \text{ with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction of } 0.25 \text{ T is acting on it in the vertical direction. What is the current flowing through the rod to keep it stationary?}$

Options:

1. $7.14 \text{ A}$
2. $5.98 \text{ A}$
3. $14.76 \text{ A}$
4. $11.32 \text{ A}$

Solution:

$iLB \cos \theta = mg \sin \theta$ $i = \left( \frac{m}{1} \right) g \tan \theta B$ $i = 0.5 \times \frac{9.8}{0.25} \times \frac{1}{\sqrt{3}}$ $i = 11.3 \text{ Amp}$

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
}