Import Question JSON

Current Question (ID: 19044)

Question:

$\text{A particle moves from } A \text{ to } B \text{ via } C \text{ with uniform speed of } \pi \text{ m/s.}$ $\text{The average velocity during the journey is:}$

Options:

1. $\sqrt{3} \text{ m/s}$
2. $\frac{\sqrt{3}}{2} \text{ m/s}$
3. $\frac{3\sqrt{3}}{2} \text{ m/s}$
4. $2 \text{ m/s}$

Solution:

$\text{Hint: } v_{\text{avg}} = \frac{\Delta x}{\Delta t}$ $\text{Step: Find the average velocity of the journey of the particle.}$ $\text{The average velocity of the particle is given by:}$ $v_{\text{avg}} = \frac{\text{Displacement}}{\text{Time taken}}$ $\text{The displacement of the particle is shown in the figure below;}$ $\text{The displacement of the particle is given by } (AB) \ 2R \sin 60^\circ \text{ as shown by the dotted line in the figure above.}$ $\text{The time taken by the particle to cover displacement } (AB, \text{ as shown by arrows in the diagram above) is given by;}$ $t = \frac{\text{distance}}{\text{velocity}} = \frac{R \times \frac{120}{360} \times 2\pi}{\pi} = \frac{2}{3} R$ $\text{Then, the average velocity of the particle is given by;}$ $v_{\text{avg}} = \frac{2R \sin 60^\circ}{\frac{2}{3} R} = \frac{3\sqrt{3}}{2}$ $\text{Hence, option (3) is the correct answer.}$

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
}