Import Question JSON

Current Question (ID: 8929)

Question:

$\text{Suppose you are riding a bike with a speed of 20 m/s due east relative to a person } A \text{ who is walking on the ground towards the east. If your friend } B \text{ walking on the ground due west measures your speed as 30 m/s due east, then the relative velocity between two reference frames } A \text{ and } B \text{ is:}$

Options:

1. $\text{the velocity of } A \text{ with respect to } B \text{ is 5 m/s towards the east.}$
2. $\text{the velocity of } A \text{ with respect to } B \text{ is 5 m/s towards the west.}$
3. $\text{the velocity of } A \text{ with respect to } B \text{ is 10 m/s towards the east.}$
4. $\text{the velocity of } A \text{ with respect to } B \text{ is 10 m/s towards the west.}$

Solution:

$\text{Hint: } \vec{v}_{XY} = \vec{v}_X - \vec{v}_Y$ $\text{Step 1: Find the velocity of the person in the frame A and B.}$ $\text{The velocity of the person in the frame A is given by:}$ $\vec{v}_{PA} = \vec{v}_P - \vec{v}_A$ $\Rightarrow \vec{v}_{PA} = 20\hat{i} \ldots (1)$ $\text{The velocity of the person in the frame B.}$ $\vec{v}_{PB} = \vec{v}_P - \vec{v}_B$ $\Rightarrow \vec{v}_{PB} = 30\hat{i} \ldots (2)$ $\text{Step 2: Find the relative velocity of the person between two reference frames A and B.}$ $\text{The velocity of A with respect to B is given by:}$ $\vec{v}_{AB} = \vec{v}_A - \vec{v}_B = 30\hat{i} - 20\hat{i} = 10\hat{i}$ $\text{Therefore, the velocity of A with respect to B is 10 m/s towards the east.}$ $\text{Hence, option (3) is the correct answer.}$

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
}