Import Question JSON

Current Question (ID: 8921)

Question:

$\text{The distance between two particles is decreasing at the rate of 6 m/sec when they are moving in the opposite directions. If these particles travel with the same initial speeds and in the same direction, then the separation increases at the rate of 4 m/sec. It can be concluded that particles' speeds could be:}$

Options:

1. $5 \text{ m/sec, } 1 \text{ m/sec}$
2. $4 \text{ m/sec, } 1 \text{ m/sec}$
3. $4 \text{ m/sec, } 2 \text{ m/sec}$
4. $5 \text{ m/sec, } 2 \text{ m/sec}$

Solution:

$\text{Hint: Use the concept of relative velocity.}$ $\text{Step: Find the velocity of the particles.}$ $\text{Let the velocity of the particle is } v_1 \text{ and } v_2\text{.}$ $\text{When two particles move towards each other, then,}$ $v_1 + v_2 = 6 \text{ m/s } \ldots (1)$ $\text{When these particles move in the same direction, then,}$ $v_1 - v_2 = 4 \text{ m/s } \ldots (2)$ $\text{By solving equations (1) and (2) we get;}$ $v_1 = 5 \text{ m/s and } v_2 = 1 \text{ m/s}$ $\text{Hence, option (1) is the correct answer.}$

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
}