Import Question JSON

Current Question (ID: 19206)

Question:

$\text{A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity } x \sqrt{F} \text{ rad s}^{-1}. \text{ If } F \text{ is the force exerted by the liquid at the other end then the value of } x \text{ will be:}$

Options:

1. $2$
2. $3$
3. $4$
4. $5$

Solution:

$\text{The force exerted by the liquid can be calculated using the formula for centrifugal force.}$ $\text{The force } F \text{ is given by } F = \frac{m \omega^2 L}{2}, \text{ where } m \text{ is the mass, } \omega \text{ is the angular velocity, and } L \text{ is the length of the tube.}$ $\text{Given } \omega = x \sqrt{F}, \text{ we substitute and solve for } x.$ $\text{After solving, we find that } x = 4.$

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
}