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Current Question (ID: 9784)

Question:

$\text{Three blocks each of mass } m \text{ are hanged vertically with the help of inextensible strings and ideal springs. Initially, the system was in equilibrium. If at any instant, the lowermost string is cut, then the acceleration of block B just after cutting the string will be:}$

Options:

1. $g$
2. $\frac{g}{2}$
3. $\frac{2g}{3}$
4. $\text{zero}$

Solution:

$\text{Hint: Just after cutting the string tension in that string becomes zero but elongation in the spring remains unchanged.}$ $\text{Step 1: Before cutting the string:}$ $\text{The tension in the string supporting block C is } T = mg$ $\text{For the equilibrium of the system, the spring must support the weight of both blocks B and C.}$ $\text{Therefore, the spring force } F = mg + mg = 2mg$ $\text{Step 2: After cutting the string:}$ $\text{When the string is cut, block C falls freely, but the spring force on block B remains } F_{sp} = 2mg \text{ (since elongation doesn't change instantly)}$ $\text{Applying Newton's second law to block B:}$ $F_{sp} - mg = ma$ $2mg - mg = ma$ $mg = ma$ $\text{Therefore, } a = g \text{ (upward)}$

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
}