Import Question JSON

Current Question (ID: 8916)

Question:

$\text{Two stones are thrown vertically up simultaneously with different velocities. Which of the following graphs represents the relative separation } (\Delta y) \text{ between them as a function of time } (t)?$

Options:

1. $\text{Graph 1: Triangular shape - linear increase then linear decrease}$
2. $\text{Graph 2: Parabolic shape opening downward}$
3. $\text{Graph 3: Exponential-like decay curve}$
4. $\text{Graph 4: Half parabola starting from origin}$

Solution:

$\text{Hint: } \vec{a}_{2,1} = \vec{a}_2 - \vec{a}_1 = 0$ $\text{Step 1: Find the relative acceleration of two stones.}$ $\text{Let their initial velocities are } u_1 \text{ \& } u_2.$ $\text{If } u_2 > u_1, u_{21} = u_2 - u_1$ $\text{\& } a_{21} = -g - (-g) = 0$ $\text{Step 2: Relate relative separation and time, using the equation of motion.}$ $\text{When both of them are in motion, the separation between them increases linearly. When the first particle comes on the ground, and the second particle is in motion, the separation between them will decrease parabolically as the height of the 2nd particle will be given by, } h = u_2 t - \frac{1}{2}gt$ $\text{Hence option (4) is correct.}$

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
}