Import Question JSON

Current Question (ID: 9889)

Question:

A ball is thrown vertically downwards from a height of \text{20 m} with an initial velocity $v_0$. It collides with the ground, loses \text{50%} of its energy in a collision and rebounds to the same height. The initial velocity $v_0$ is: (Take $g = 10 \text{ ms}^{-2}$)

Options:

1. $14 \text{ ms}^{-1}$
2. $20 \text{ ms}^{-1}$
3. $28 \text{ ms}^{-1}$
4. $10 \text{ ms}^{-1}$

Solution:

$\text{Suppose a ball rebounds with speed } v\text{,}$ $v = \sqrt{2gh} = \sqrt{2 \times 10 \times 20} = 20 \text{ m/s}$ $\text{Energy of a ball just after the rebound,}$ $E = \frac{1}{2}mv^2 = 200m$ $\text{where } m \text{ is the mass of the ball.}$ $\text{As 50% of energy is lost in the collision means just before the collision, the energy is 400m. According to the law of conservation of energy, we have,}$ $\frac{1}{2}mv_0^2 + mgh = 400m$ $\frac{1}{2}mv_0^2 + m \times 10 \times 20 = 400m$ $v_0 = 20 \text{ m/s}$

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
}