Import Question JSON

Current Question (ID: 19184)

Question:

$\text{A boy ties a stone of mass } 100 \text{ g to the end of a } 2 \text{ m long string and whirls it around in a horizontal plane.}$ $\text{The string can withstand the maximum tension of } 80 \text{ N.}$ $\text{If the maximum speed with which the stone can revolve is } \frac{K}{\pi} \text{ rev./min.}$ $\text{The value of } K \text{ is: (Assume the string is massless and unstretchable)}$

Options:

1. 400
2. 300
3. 600
4. 800

Solution:

$\text{The tension in the string provides the centripetal force required for circular motion.}$ $\text{Centripetal force } F = \frac{mv^2}{r}$ $\text{Given: } m = 0.1 \text{ kg, } r = 2 \text{ m, } F = 80 \text{ N}$ $80 = \frac{0.1 \times v^2}{2}$ $v^2 = 1600$ $v = 40 \text{ m/s}$ $\text{The angular velocity } \omega = \frac{v}{r} = \frac{40}{2} = 20 \text{ rad/s}$ $\text{Convert to revolutions per minute:}$ $\omega = \frac{20}{2\pi} \text{ rev/s} = \frac{20 \times 60}{2\pi} \text{ rev/min}$ $= \frac{600}{\pi} \text{ rev/min}$ $\text{Thus, } K = 600$

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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
}