Import Question JSON

Current Question (ID: 9731)

Question:

$\text{A mass of 4 kg is suspended as shown in the figure with the help of massless inextensible string } A\text{. Another identical string, } B\text{, is connected at the lower end of the block. When a sudden pulling downward jerk slightly greater than the breaking strength of } A \text{ and } B \text{ is given to string } B\text{, then:}$

Options:

1. $\text{String } A \text{ will break.}$
2. $\text{String } B \text{ will break.}$
3. $\text{Both } A \text{ and } B \text{ will break simultaneously.}$
4. $\text{Both } A \text{ and } B \text{ will never break.}$

Solution:

$\text{Hint: Use the concept of inertia.}$ $F = \frac{\Delta p}{\Delta t}$ $\Delta p = F \Delta t \approx 0$ $\text{Hence string B will break.}$ $\text{Explanation: When a sudden jerk is applied to string B, the mass of 4 kg cannot respond instantaneously due to its inertia. The sudden force creates a large tension in string B, but the mass above remains relatively stationary for the brief moment of the jerk. Since the jerk force is applied directly to string B and the mass cannot immediately accelerate due to inertia, string B experiences the full force and breaks first.}$

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
}