Import Question JSON

Current Question (ID: 9781)

Question:

$\text{Three blocks } A, B \text{ and } C \text{ of mass } 3M, 2M \text{ and } M \text{ respectively are suspended vertically with the help of springs } PQ \text{ and } TU \text{ and a string } RS \text{ as shown in Figure. The acceleration of blocks } A, B \text{ and } C \text{ are } a_1, a_2 \text{ and } a_3 \text{ respectively. The value of acceleration } a_1 \text{ at the moment string } RS \text{ is cut will be:}$

Options:

1. $g \text{ downward}$
2. $g \text{ upward}$
3. $\text{more than } g \text{ downward}$
4. $\text{zero}$

Solution:

\text{Before cutting the string RS:} \text{The spring PQ supports all three blocks, so the spring force } F_{s1} = (3M + 2M + M)g = 6Mg \text{The system is in equilibrium with the spring force balancing the total weight.} \text{After cutting the string RS:} \text{Block A becomes isolated from blocks B and C. The spring force } F_{s1} = 6Mg \text{ remains the same} \text{(since spring extension doesn't change instantaneously).} \text{For block A: Net upward force} = F_{s1} - 3Mg = 6Mg - 3Mg = 3Mg \text{Using Newton's second law: } 3Mg = 3M \cdot a_1 \text{Therefore: } a_1 = \frac{3Mg}{3M} = g \text{ (upward)}

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
}