Import Question JSON

Current Question (ID: 10186)

Question:

$\text{A particle of mass m moves with a constant velocity along 3 different paths, DE, OA and BC. Which of the following statements is not correct about its angular momentum about point O?}$

Options:

1. $\text{It is zero when it is at A and moving along OA.}$
2. $\text{The same at all points along the line DE.}$
3. $\text{Of the same magnitude but oppositely directed at B and D.}$
4. $\text{Increases as it moves along the line BC.}$

Solution:

$\text{Angular momentum = momentum × perpendicular distance.}$ $\text{For motion along BC, perpendicular distance does not alter.}$ $\text{Since the particle moves with constant velocity, its momentum remains constant. When moving along BC (which is vertical), the perpendicular distance from point O to the line BC remains constant at 1m throughout the motion. Therefore, the angular momentum remains constant and does not increase as it moves along BC.}$ $\text{Statement 4 is incorrect because angular momentum is constant along BC, not increasing.}$

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
}