Import Question JSON

Current Question (ID: 9820)

Question:

$\text{A mass } m \text{ is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:}$

Options:

1. $\text{inclined at a } 60^\circ \text{ angle from vertical}$
2. $\text{the mass is at the highest point}$
3. $\text{the wire is horizontal}$
4. $\text{the mass is at the lowest point}$

Solution:

In vertical circular motion, the tension in the wire varies with position due to the combined effects of centripetal force and gravitational force. At the lowest point of the circle, the tension must provide both: 1. The centripetal force needed to keep the mass moving in a circle: mv²/r 2. Support the weight of the mass against gravity: mg Therefore, at the lowest point: T = mv²/r + mg At the highest point, gravity helps provide the centripetal force, so: T = mv²/r - mg Since the tension is maximum at the lowest point, this is where the wire is most likely to break.

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
}