Import Question JSON

Current Question (ID: 10228)

Question:

$\text{A bomb is projected from the ground at a horizontal range of } R. \text{ If the bomb explodes mid-air, then the range of its centre of mass is:}$

Options:

1. $\frac{R}{2}$
2. $R$
3. $2R$
4. $\frac{2R}{3}$

Solution:

$\text{When a bomb (or any projectile) explodes in mid-air, the internal forces of the explosion do not affect the motion of its center of mass. In the absence of external forces (like air resistance, which is usually neglected in such problems unless stated otherwise), the center of mass continues to follow the same parabolic trajectory it would have followed had no explosion occurred.}$ $\text{Therefore, if the bomb was projected to have a horizontal range of } R, \text{ its center of mass will still reach the same horizontal range } R.$ $\text{The final answer is option 2.}$

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
}