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Current Question (ID: 19392)

Question:

$\text{A body is rotating with kinetic energy, } E. \text{ If the angular velocity of the body is increased to three times of the initial angular velocity then kinetic energy becomes } nE. \text{ What would be the value of } n?$

Options:

1. $3$
2. $7$
3. $9$
4. $5$

Solution:

$\text{Hint: } K.E. = \frac{1}{2} I \omega^2$ $\text{Step: Find the value of } n.$ $\text{The initial rotational kinetic energy is given by:}$ $K.E = \frac{1}{2} I \omega^2 = E \quad \ldots (1)$ $\text{When angular velocity increased to three times the initial angular velocity then the rotational kinetic energy is given by:}$ $nE = \frac{1}{2} I (3\omega)^2 = 9 \left( \frac{1}{2} I \omega^2 \right) \quad \ldots (2)$ $\text{From (1) and (2) we get:}$ $\Rightarrow 9E = nE \Rightarrow n = 9$ $\text{Hence, option (3) is the correct answer.}$

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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
}