Import Question JSON

Current Question (ID: 19987)

Question:

$\text{Two wires } W_1 \text{ and } W_2 \text{ have the same radius } r \text{ and respective densities } \rho_1 \text{ and } \rho_2 \text{ such that } \rho_2 = 4\rho_1. \text{ They are joined together at the point } O, \text{ as shown in the figure. The combination is used as a sonometer wire and kept under tension } T. \text{ The point } O \text{ is midway between the two bridges. When a stationary wave is set up in the composite wire, the joint is found to be a node. The ratio of the number of antinodes formed in } W_1 \text{ to } W_2 \text{ is:}$

Options:

1. $4 : 1$
2. $1 : 1$
3. $1 : 2$
4. $1 : 3$

Solution:

$\text{Hint: } n = \frac{p}{2l} \sqrt{\frac{T}{\pi r^2 \rho}}$

Import JSON File

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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
}