Import Question JSON

Current Question (ID: 19235)

Question:

$\text{Two particles, of masses } M \text{ and } 2M, \text{ moving, as shown, with speeds of } 10 \text{ m/s and } 5 \text{ m/s, collide elastically at the origin.}$ $\text{After the collision, they move along the indicated directions with speeds } v_1 \text{ and } v_2, \text{ respectively.}$ $\text{The values of } v_1 \text{ and } v_2 \text{ are nearly:}$

Options:

1. $3.2 \text{ m/s and } 12.6 \text{ m/s}$
2. $3.2 \text{ m/s and } 6.3 \text{ m/s}$
3. $6.5 \text{ m/s and } 6.3 \text{ m/s}$
4. $6.5 \text{ m/s and } 3.2 \text{ m/s}$

Solution:

$\text{Hint: Conserve momentum along the horizontal direction.}$ $\text{Using momentum conservation in x direction}$ $m \times 10 \cos 30^\circ + 2m \cos 45^\circ = mv_2 \cos 45^\circ + 2m \ v_1 \cos 30^\circ$ $\text{In y direction}$ $2m \times 5 \sin 45^\circ - m \times 10 \sin 30^\circ = 2m \ v_1 \sin 30^\circ - mv_2 \sin 45^\circ$ $\text{Solving equation } v_1 = 6.5 \text{ m/s, } v_2 = 6.3 \text{ m/s}$

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
}