Import Question JSON

Current Question (ID: 9624)

Question:

$\text{A shell is fired vertically upward with a velocity of 20 m/s from a trolley moving horizontally with a velocity of 10 m/s. A person on the ground observes the motion of the shell like a parabola whose horizontal range is: } (g = 10 \text{ m/s}^2)$

Options:

1. $20 \text{ m}$
2. $10 \text{ m}$
3. $40 \text{ m}$
4. $400 \text{ m}$

Solution:

\text{Hint: In the horizontal direction, } v_{\text{shell}} = v_{\text{trolley}} \text{Step 1: Find the initial velocity of shell w.r.t ground} u_x = 10 \text{ m/s} u_y = 20 \text{ m/s} \text{Step 2: Find the range of the projectile.} R = \frac{2u_x u_y}{g} = \frac{2 \times 10 \times 20}{10} = 40 \text{ m} \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
}