Import Question JSON

Current Question (ID: 8877)

Question:

$\text{A helicopter moving vertically upwards releases a packet when it is at a certain height above the ground. The packet initially moves upwards for a time } t_1 \text{ and then falls downwards for a time } t_2 \text{ until it reaches the ground. Then:}$

Options:

1. $t_1 < t_2$
2. $t_1 = t_2$
3. $t_1 > t_2$
4. $\text{Data insufficient}$

Solution:

$\text{Hint: The packet covers more distance in the downward direction}$ $\text{Step 1: Draw the path of motion of the packet}$ $\text{The packet follows a parabolic path, moving upward from point A to maximum height B, then falling downward from B to the ground.}$ $\text{Step 2: Compare times for upward \& downward motion}$ $\text{Since the packet covers more distance in the downward direction than in the upward direction, and both motions occur under the same gravitational acceleration, the time for downward motion is greater.}$ $\text{Thus, } t_1 < t_2$ $\text{Hence, option (1) is the correct answer.}$

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
}