Import Question JSON

Current Question (ID: 9674)

Question:

$\text{A boat is moving with a velocity } 3\hat{i} + 4\hat{j} \text{ with respect to ground. The water in the river is moving with a velocity } -3\hat{i} - 4\hat{j} \text{ with respect to ground. The relative velocity of the boat with respect to water is:}$

Options:

1. $8\hat{j}$
2. $-6\hat{i} - 8\hat{j}$
3. $6\hat{i} + 8\hat{j}$
4. $5\sqrt{2}$

Solution:

\text{Hint: } \vec{v}_{B,W} = \vec{v}_{B,G} - \vec{v}_{W,G} \text{Step: Find the relative velocity of the boat with respect to water.} \text{The relative velocity of the boat with respect to the water can be found using:} \vec{v}_{\text{boat, water}} = \vec{v}_{\text{boat, ground}} - \vec{v}_{\text{water, ground}} \vec{v}_{B,W} = \vec{v}_{B,G} - \vec{v}_{W,G} \text{Substitute the known values we get:} \vec{v}_{B,W} = 3\hat{i} + 4\hat{j} - (-3\hat{i} - 4\hat{j}) \Rightarrow \vec{v}_{B,W} = 3\hat{i} + 4\hat{j} + 3\hat{i} + 4\hat{j} \Rightarrow \vec{v}_{B,W} = 6\hat{i} + 8\hat{j} \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
}