Import Question JSON

Current Question (ID: 9814)

Question:

$\text{A stone of mass } m \text{ tied to the end of a string revolves in a vertical circle of radius } R. \text{ The magnitude of net forces at the lowest and highest points of the circle directed vertically downwards are:}$ $\text{(}T_1 \text{ and } v_1 \text{ denote the tension and speed at the lowest point. } T_2 \text{ and } v_2 \text{ denote corresponding values at the highest point.)}$

Options:

1. $\text{Lowest point: } mg - T_1, \text{ Highest point: } mg + T_2$
2. $\text{Lowest point: } mg + T_1, \text{ Highest point: } mg + T_2$
3. $\text{Lowest point: } mg + T_1 - \frac{mv_1^2}{R}, \text{ Highest point: } mg - T_2 + \frac{mv_2^2}{R}$
4. $\text{Lowest point: } mg - T_1 - \frac{mv_1^2}{R}, \text{ Highest point: } mg + T_2 + \frac{mv_2^2}{R}$

Solution:

$\text{Note: Solution image not provided. Based on physics principles:}$ $\text{At the lowest point, weight acts downward and tension acts upward toward the center.}$ $\text{Net downward force = } mg - T_1$ $\text{At the highest point, both weight and tension act downward toward the center.}$ $\text{Net downward force = } mg + T_2$

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
}