Import Question JSON

Current Question (ID: 9780)

Question:

$\text{Two blocks, A and B, of masses } 2m \text{ and } 4m \text{ are connected by a string. The block of mass } 4m \text{ is connected by a spring (massless). The string is suddenly cut. The ratio of the magnitudes of accelerations of masses } 2m \text{ and } 4m \text{ at that instant will be:}$

Options:

1. $1 : 2$
2. $2 : 1$
3. $1 : 4$
4. $4 : 1$

Solution:

$\text{Hint: When the string is cut, block A will fall freely.}$ $\text{Step 1: Find spring force, } F_s$ $\text{The spring force equals the weight of the combined system before cutting:}$ $F_s = 6mg$ $\text{Step 2: Find } a_A \text{ and } a_B$ $\text{For block A (mass } 2m\text{): After the string is cut, block A falls freely under gravity}$ $a_A = g$ $\text{For block B (mass } 4m\text{): The spring force acts upward, weight acts downward}$ $F_s - 4mg = 4m \cdot a_B$ $6mg - 4mg = 4m \cdot a_B$ $2mg = 4m \cdot a_B$ $a_B = \frac{g}{2}$ $\text{Step 3: Find the ratio of accelerations of blocks A and B}$ $\frac{a_A}{a_B} = \frac{g}{\frac{g}{2}} = \frac{g \cdot 2}{g} = 2$ $\text{Therefore, the ratio } a_A : a_B = 2 : 1$

Import JSON File

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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
}