Import Question JSON

Current Question (ID: 20385)

Question:

$\text{A conducting rod, suspended freely in a gravitational field, carries a current } I \text{ as shown in the figure. If the length of the rod, current in the rod, and magnetic field strength are } 0.5 \text{ m, } 2 \text{ A, and } 0.4 \text{ T respectively, the mass of the rod is: (take } g = 10 \text{ m/s}^2)$

Options:

1. $20 \text{ grams}$
2. $40 \text{ grams}$
3. $60 \text{ grams}$
4. $80 \text{ grams}$

Solution:

$\text{Hint: } F = BIL$ $\text{Step: Find the mass of the rod.}$ $\text{The force acting on the rod is shown in the figure below;}$ $\text{The magnetic force acting on the rod is balanced by the weight of the rod i.e., } F_B = mg$ $\Rightarrow BIL = mg$ $\Rightarrow m = \frac{BIL}{g} = \frac{0.5 \times 2 \times 0.4}{10}$ $\Rightarrow m = \frac{4}{100} = 40 \text{ g}$ $\text{Therefore, the mass of the rod is } 40 \text{ g.}$ $\text{Hence, option (2) is the correct answer.}$

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
}