Import Question JSON

Current Question (ID: 10202)

Question:

$\text{Particles } A \text{ and } B \text{ are separated by 10 m, as shown in the figure. If } A \text{ is at rest and } B \text{ started moving with a speed of 20 m/s then the angular velocity of } B \text{ with respect to } A \text{ at that instant is:}$

Options:

1. $1 \text{ rad/s}$
2. $1.5 \text{ rad/s}$
3. $2 \text{ rad/s}$
4. $2.5 \text{ rad/s}$

Solution:

\text{1. Identify the relevant quantities:} \text{• Distance between A and B, } r = 10 \text{ m} \text{• Speed of B, } v_B = 20 \text{ m/s} \text{• Angle between the velocity vector of B and the line AB is } 30° \text{2. Find the component of } v_B \text{ perpendicular to the line AB (}v_{\perp}\text{):} \text{The line AB is horizontal. The velocity vector of B makes an angle of } 30° \text{ with the horizontal.} \text{Therefore, the component of } v_B \text{ perpendicular to AB is } v_{\perp} = v_B \sin(30°) v_{\perp} = 20 \text{ m/s} \times \sin(30°) = 20 \text{ m/s} \times 0.5 = 10 \text{ m/s} \text{3. Calculate the angular velocity (}\omega\text{):} \text{The angular velocity is given by the formula } \omega = \frac{v_{\perp}}{r} \omega = \frac{10 \text{ m/s}}{10 \text{ m}} = 1 \text{ rad/s} \text{The final answer is } 1 \text{ rad/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
}