Import Question JSON

Current Question (ID: 8858)

Question:

$\text{A ball is thrown vertically downwards with a velocity of 20 m/s from the top of a tower. It hits the ground after some time with the velocity of 80 m/s. The height of the tower is: (assuming } g = 10 \text{ m/s}^2\text{)}$

Options:

1. $340 \text{ m}$
2. $320 \text{ m}$
3. $300 \text{ m}$
4. $360 \text{ m}$

Solution:

$\text{Hint: } v^2 = u^2 + 2as$ $\text{Step: Find the height of the tower.}$ $\text{Given: } v = 80 \text{ m/s}, u = 20 \text{ m/s}, a = 10 \text{ m/s}^2$ $\text{According to the third equation of motion, we have:}$ $v^2 = u^2 + 2as$ $\Rightarrow (80)^2 = (20)^2 + 2 \times 10 \times h$ $\Rightarrow h = \frac{6400 - 400}{20} = \frac{6000}{20} = 300 \text{ m}$ $\text{Therefore, the height of the tower is 300 m.}$ $\text{Hence, option (3) is the correct answer.}$

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
}