Import Question JSON

Current Question (ID: 9782)

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:

\text{Mass of block A} = 3m, \text{Mass of block B} = m \text{Before cutting the string:} \text{Force equations are:} kx = T + 3mg \quad \text{...(i)} T = mg \quad \text{...(ii)} \text{From equations (i) and (ii):} kx = mg + 3mg = 4mg \text{After cutting the string: } T = 0 \text{The spring force remains } kx = 4mg \text{ (since extension doesn't change instantaneously)} \text{For block A: Net upward force} = 4mg - 3mg = mg \text{Acceleration of block A} = \frac{mg}{3m} = \frac{g}{3} \text{ (upward)} \text{For block B: Only weight acts downward} \text{Acceleration of block B} = \frac{mg}{m} = g \text{ (downward)}

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
}