Import Question JSON

Current Question (ID: 8805)

Question:

$\text{A body is projected vertically upwards with a speed } v. \text{ The distance travelled by the body in the last second of upward journey is the same as that of:}$

Options:

1. $\text{distance travelled in last second of downward journey}$
2. $\text{distance travelled in first second of upward journey}$
3. $\text{distance travelled in first second of downward journey}$
4. $\text{both (1) and (2)}$

Solution:

\textbf{Hint:} \text{ Upward and downward motions are symmetric with respect to each other.} \textbf{Step 1:} \text{ Visualize the motion using symmetry.} \text{The motion can be represented with time intervals marked as 1st, 2nd, 3rd, 4th seconds for upward journey, and 5th, 6th, 7th, 8th seconds for downward journey.} \textbf{Step 2:} \text{ Find the distance travelled by the body in the last second.} \text{Due to symmetry of motion, the distance travelled by the body in the last second of the upward journey is the same as the distance travelled in the first second of the downward journey.} \text{Hence, Option (3) 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
}