Import Question JSON

Current Question (ID: 9862)

Question:

$\text{What is the work done by gravity on block A in 2 seconds after the blocks are released? (Pulley is light)}$

Options:

1. $240 \text{ J}$
2. $200 \text{ J}$
3. $120 \text{ J}$
4. $24 \text{ J}$

Solution:

\text{For the pulley system with block A (6 kg) and block B (4 kg):} \text{Net force on the system} = (m_A - m_B)g = (6 - 4) \times 10 = 20 \text{ N} \text{Total mass} = m_A + m_B = 6 + 4 = 10 \text{ kg} \text{Acceleration} = \frac{\text{Net force}}{\text{Total mass}} = \frac{20}{10} = 2 \text{ m/s}^2 \text{Distance moved by block A in 2 seconds:} s = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2} \times 2 \times (2)^2 = 4 \text{ m} \text{Work done by gravity on block A} = m_A g s = 6 \times 10 \times 4 = 240 \text{ J} \text{The work done by gravity on block A is 240 J.}

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
}