Import Question JSON

Current Question (ID: 19305)

Question:

$\text{A particle of mass } m \text{ moving with velocity } v \text{ collides with a stationary}$ $\text{particle of mass } 2m \text{ and sticks to it. The velocity of the combined}$ $\text{mass (system) will be:}$

Options:

1. $v$
2. $\frac{v}{2}$
3. $\frac{v}{3}$
4. $\frac{v}{4}$

Solution:

$\text{Apply the conservation of momentum.}$ $\text{Find the velocity of the combined mass system.}$ $\text{Let the velocity of the combined mass system is } v' \text{ m/s.}$ $\text{Apply conservation of linear momentum, we get;} \newline \Rightarrow mv = (m + 2m)v'$ $\Rightarrow v' = \frac{v}{3}$ $\text{Therefore, the velocity of the combined mass system is } \frac{v}{3}. \text{Hence, option (3) is the correct answer.}$

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
}