Import Question JSON

Current Question (ID: 9815)

Question:

$\text{The angle between the position vector and the acceleration vector of a particle in non-uniform circular motion (centre of the circle is taken as the origin) will be:}$

Options:

1. $0°$
2. $45°$
3. $75°$
4. $135°$

Solution:

$\text{Hint: Here net acceleration is the resultant of tangential acceleration and centripetal acceleration.}$ $\text{Step 1: As centripetal acceleration is towards the center of the circle and tangential is along the tangent. Thus, the direction of angle between position vector and acceleration vector is shown in the figure.}$ $\text{Step 2: The acceleration vector always makes more than a } 90° \text{ angle with the position vector in a non-uniform circular motion.}$

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
}