Import Question JSON

Current Question (ID: 9887)

Question:

$\text{If a stone is projected vertically upward from the ground at a speed of 10 m/s, then it's: } (g = 10 \text{ m/s}^2)$

Options:

1. $\text{Potential energy will be maximum after 0.5 s}$
2. $\text{Kinetic energy will be maximum again after 1 s}$
3. $\text{Kinetic energy = potential energy at a height of 2.5 m from the ground}$
4. $\text{Potential energy will be minimum after 1 s}$

Solution:

$\text{Step 1: Find the time of maximum height.}$ $v = u - gt$ $0 = 10 - 10t$ $t = 1s$ $\text{Step 2: Find the maximum height reached by the particle.}$ $\text{At the maximum height,}$ $\frac{1}{2}mv^2 = mgh$ $h = \frac{v^2}{2g} = \frac{10^2}{2 \times 10} = 5m$ $\text{Step 3: Find the height when the potential energy and the kinetic energy are equal to each other.}$ $\text{The potential energy will be equal to the kinetic energy when}$ $h = \frac{h_{max}}{2} = 2.5m$

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
}