Import Question JSON

Current Question (ID: 19288)

Question:

$\text{Three blocks } A, B \text{ and } C \text{ are lying on a smooth horizontal surface, as shown in the figure. } A \text{ and } B \text{ have equal masses, } m \text{ while } C \text{ has mass } M. \text{ Block } A \text{ is given an initial speed } v \text{ towards } B \text{ due to which it collides with } B \text{ perfectly inelastically. The combined mass collides with } C, \text{ also perfectly inelastically if } \frac{5}{6} \text{ th of the initial kinetic energy is lost in the whole process. The value of } (M/m) \text{ is:}$

Options:

1. $5$
2. $2$
3. $4$
4. $3$

Solution:

$\text{Hint: Conserve the linear momentum.}$

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
}