Import Question JSON

Current Question (ID: 19219)

Question:

$A \ 1 \ \text{kg} \ \text{mass is suspended from the ceiling by a rope of length} \ 4 \ \text{m.}$ $\text{A horizontal force} \ 'F' \ \text{is applied at the midpoint of the rope so that the rope makes an angle of} \ 45^\circ \ \text{with respect to the vertical axis as shown in figure.}$ $\text{The magnitude of} \ F \ \text{is: (Assume that the system is in equilibrium and} \ g = 10 \ \text{m/s}^2)$

Options:

1. $10 \ \text{N}$
2. $1 \ \text{N}$
3. $\frac{10}{\sqrt{2}} \ \text{N}$
4. $\frac{1}{10 \times \sqrt{2}} \ \text{N}$

Solution:

$\text{In equilibrium, the vertical component of} \ T_1 \ \text{balances the weight:}$ $T_1 \cos 45^\circ = 1 \times 10$ $T_1 \times \frac{1}{\sqrt{2}} = 10$ $T_1 = 10 \sqrt{2}$ $\text{The horizontal component of} \ T_1 \ \text{balances} \ F:$ $T_1 \sin 45^\circ = F$ $10 \sqrt{2} \times \frac{1}{\sqrt{2}} = F$ $F = 10 \ \text{N}$

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
}