Import Question JSON

Current Question (ID: 19218)

Question:

$\text{A light unstretchable string passing over a smooth light pulley connects two blocks of masses } m_1 \text{ and } m_2. \text{ If the acceleration of the system is } \frac{g}{8}, \text{ then the ratio of the masses } \frac{m_2}{m_1} \text{ is:}$

Options:

1. $4 : 3$
2. $5 : 3$
3. $8 : 1$
4. $9 : 7$

Solution:

$\text{Let the tension in the string be } T. \text{ For } m_1, \text{ we have } T - m_1g = m_1a. \text{ For } m_2, \text{ we have } m_2g - T = m_2a. \text{ Adding these equations: } m_2g - m_1g = (m_1 + m_2)a. \text{ Given } a = \frac{g}{8}, \text{ so } m_2g - m_1g = (m_1 + m_2)\frac{g}{8}. \text{ Simplifying gives } 8(m_2 - m_1) = m_1 + m_2. \text{ Solving for } \frac{m_2}{m_1}, \text{ we get } \frac{m_2}{m_1} = \frac{9}{7}.$

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
}