Import Question JSON

Current Question (ID: 9608)

Question:

$\text{The velocity of a projectile at the initial point } A \text{ is } 2\hat{i} + 3\hat{j} \text{ m/s. Its velocity (in m/s) at the point } B \text{ is:}$

Options:

1. $-2\hat{i} + 3\hat{j}$
2. $2\hat{i} - 3\hat{j}$
3. $2\hat{i} + 3\hat{j}$
4. $-2\hat{i} - 3\hat{j}$

Solution:

\text{Hint: Use } \vec{v} = v_x \hat{i} + v_y \hat{j} \text{Step: Find the velocity at point B} \text{As the velocity of the projectile at point A is given by: } 2\hat{i} + 3\hat{j} \text{While coming at point B, the x-component of the velocity will be in the positive x direction} \text{ and the y-component of the velocity will be in the negative y direction as shown in figure.} \text{Therefore, velocity at point B is given by: } 2\hat{i} - 3\hat{j} \text{Hence, option (2) 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
}