Import Question JSON

Current Question (ID: 9790)

Question:

$\text{A particle of mass } m \text{ is suspended from a ceiling through a massless string. The particle moves in a horizontal circle as shown in the given figure. The tension in the string is:}$

Options:

1. $mg$
2. $2mg$
3. $3mg$
4. $4mg$

Solution:

$\text{Hint: Balance the vertical forces.}$ $\text{Step 1: Draw a free body diagram.}$ $\text{The diagram shows the particle with tension } T \text{ acting along the string at } 60° \text{ from vertical, weight } mg \text{ acting downward, and the horizontal component } T\sin 60° \text{ providing centripetal force.}$ $\text{Step 2: Find the tension in the string.}$ $\text{For vertical equilibrium:}$ $T \cos 60° = mg$ $T = \frac{mg}{\cos 60°} = \frac{mg}{0.5} = 2mg$

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
}