Import Question JSON

Current Question (ID: 19372)

Question:

$\text{A solid cylinder is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbinding, for the strings to achieve a speed of } 4 \text{ ms}^{-1}, \text{ is:}$ $\text{(take } g = 10 \text{ ms}^{-2})$

Options:

1. $100 \text{ cm}$
2. $110 \text{ cm}$
3. $120 \text{ cm}$
4. $130 \text{ cm}$

Solution:

$\text{Hint: Apply conservation of energy.}$ $\text{Step: Find the distance from the initial rest position.}$ $\text{Apply the conservation of energy we get;} \ mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\omega^2$ $\text{The distance from the initial rest position is given by;} \ mgh = \frac{1}{2}mv^2 + \frac{1}{2}\frac{mR^2}{2}\omega^2 \quad \left[ I = \frac{mR^2}{2} \right] \quad \left[ v = R\omega \right]$ $\Rightarrow 10h = \frac{16}{2} + \frac{16}{4}$ $\Rightarrow h = 1.2 \text{ m} = 120 \text{ cm}$ $\text{Hence, option (3) is the correct answer.}$

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
}