Import Question JSON

Current Question (ID: 19022)

Question:

$\text{A particle starts from origin } O \text{ from rest and moves with a uniform acceleration along the positive } x\text{-axis. Identify all figures that correctly represent the motion qualitatively.}$ $(a = \text{acceleration}, \ v = \text{velocity}, \ x = \text{displacement}, \ t = \text{time})$

Options:

1. $(A) \text{ only}$
2. $(A), \ (B) \text{ and } (D) \text{ only}$
3. $(B) \text{ and } (C) \text{ only}$
4. $(A), \ (B) \text{ and } (C) \text{ only}$

Solution:

$\text{Hint: } v = u + at$ $\text{Explanation: The particle starts from rest at the origin and moves with uniform acceleration along the positive } x\text{-axis.}$ $\text{The relationships between the quantities are:}$ $\text{Displacement-Time } (x-t): \text{ For uniform acceleration, displacement increases quadratically with time } (s = ut + \frac{1}{2} at^2).$ $\text{Therefore, the graph of } (x-t) \text{ should be a parabola opening upwards. (D) Likely represents } (x-t) \text{ (parabolic graph).}$ $\text{Velocity-Time } (v-t): \text{ Since the particle starts from rest and accelerates uniformly, the velocity will increase linearly with time } (v = u + at), \text{ which means the graph of } (v-t) \text{ should be a straight line with a positive slope. (B) Likely represents } (v-t) \text{ (linear graph).}$ $\text{Acceleration-Time } (a-t): \text{ The particle experiences uniform acceleration } (a = \text{constant}), \text{ so the graph of } (a-t) \text{ should be a horizontal line. (A) Likely represents } (a-t) \text{ (horizontal line).}$ $\text{Hence, option } (2) \text{ is the correct answer.}$

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
}