Import Question JSON

Current Question (ID: 19298)

Question:

$\text{A man of } 60 \text{ kg is running on the road and suddenly jumps into a stationary trolly car of mass } 120 \text{ kg.}$ $\text{Then, the trolly car starts moving with a velocity of } 2 \text{ ms}^{-1}. \text{ The velocity of the running man just before jumping into trolly car was:}$

Options:

1. $4 \text{ ms}^{-1}$
2. $2 \text{ ms}^{-1}$
3. $3 \text{ ms}^{-1}$
4. $6 \text{ ms}^{-1}$

Solution:

$\text{Hint: Take the system as man and trolley and conserve the momentum.}$ $\text{Step: Find the momentum of the man.}$ $\text{The initial momentum of the man } = 60v$ $\text{The final momentum of the system } = (60 + 120) \times 2$ $\text{Apply conservation of momentum.}$ $(60 + 120) \times 2 = 60v$ $\Rightarrow v = 6 \text{ ms}^{-1}$

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
}