Import Question JSON

Current Question (ID: 9819)

Question:

$\text{A massless and inextensible string connects two blocks A and B of masses } 3m \text{ and } m, \text{ respectively. The whole system is suspended by a massless spring, as shown in the figure. The magnitudes of acceleration of A and B immediately after the string is cut, are respectively:}$

Options:

1. $\frac{g}{3}, g$
2. $g, g$
3. $\frac{g}{3}, \frac{g}{3}$
4. $g, \frac{g}{3}$

Solution:

Before the string is cut, the system is in equilibrium. The spring force balances the total weight: F_{\text{spring}} = (3m + m)g = 4mg When the string is cut, both blocks experience different forces: For block A (mass 3m): The spring force F_{\text{spring}} = 4mg acts upward, and weight 3mg acts downward. Net force on A: F_{\text{net,A}} = 4mg - 3mg = mg (upward) Acceleration of A: a_A = \frac{F_{\text{net,A}}}{3m} = \frac{mg}{3m} = \frac{g}{3} (upward) For block B (mass m): Only weight mg acts downward (no spring force or tension). Net force on B: F_{\text{net,B}} = mg (downward) Acceleration of B: a_B = \frac{F_{\text{net,B}}}{m} = \frac{mg}{m} = g (downward) Therefore, the magnitudes of acceleration are \frac{g}{3} and g respectively.

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
}