Import Question JSON

Current Question (ID: 9669)

Question:

$\text{A particle moves with constant angular velocity in a circle. During the motion its:}$

Options:

1. $\text{Energy is conserved}$
2. $\text{Momentum is conserved}$
3. $\text{Energy and momentum both are conserved}$
4. $\text{None of the above is conserved}$

Solution:

\text{In uniform circular motion (constant angular velocity) kinetic energy remains constant but due to change in velocity of particle its momentum varies.} \text{Analysis:} \text{Energy: The kinetic energy } KE = \frac{1}{2}mv^2 \text{ remains constant since the speed } |v| \text{ is constant in uniform circular motion.} \text{Momentum: The momentum } \vec{p} = m\vec{v} \text{ changes continuously because the velocity vector } \vec{v} \text{ changes direction even though its magnitude remains constant.} \text{Therefore, energy is conserved but momentum is not conserved in 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
}