Import Question JSON

Current Question (ID: 19217)

Question:

$\text{A player caught a cricket ball of mass } 150 \text{ g moving at a speed of } 20 \text{ m/s.}$ $\text{If the catching process is completed in } 0.1 \text{ s, the magnitude of force exerted by the ball on the hand of the player is:}$

Options:

1. $150 \text{ N}$
2. $3 \text{ N}$
3. $30 \text{ N}$
4. $300 \text{ N}$

Solution:

$\text{Given: } m = 150 \text{ g} = 0.15 \text{ kg}, \ v = 20 \text{ m/s}, \ \Delta t = 0.1 \text{ s}$ $\text{Force, } F = \frac{\Delta p}{\Delta t} = \frac{m(v_f - v_i)}{\Delta t}$ $\text{Since the ball comes to rest, } v_f = 0$ $F = \frac{0.15 \times (0 - 20)}{0.1} = \frac{-3}{0.1} = -30 \text{ N}$ $\text{Magnitude of force is } 30 \text{ N}$

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
}