Import Question JSON

Current Question (ID: 9663)

Question:

$\text{Which of the following statement/s is/are incorrect regarding the motion in a plane?}$

Options:

1. $\text{a body can't move on a curved path with constant acceleration.}$
2. $\text{the angle between acceleration and velocity can be 90°.}$
3. $\text{the angle between acceleration and velocity can be other than 90°.}$
4. $\text{all of the above.}$

Solution:

\text{Hint - In projectile motion, } \vec{a} = -g\hat{j} \text{Step 1: Check all options} \text{1) A body can move on a curved path with constant acceleration} \text{(projectile motion shows this). This statement is incorrect.} \text{2) In uniform circular motion, acceleration is perpendicular to velocity,} \text{so the angle can be 90°. This statement is correct.} \text{Therefore, only statement 1 is incorrect.}

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
}