Import Question JSON

Current Question (ID: 19186)

Question:

$\text{An object of mass 5 kg is thrown vertically upwards from the ground.}$ $\text{The air resistance produces a constant retarding force of 10 N}$ $\text{throughout the motion. The ratio of time of ascent to the descent will}$ $\text{be equal to: [Use } g = 10 \text{ ms}^{-2}]$

Options:

1. $1 : 1$
2. $\sqrt{2} : \sqrt{3}$
3. $\sqrt{3} : \sqrt{2}$
4. $2 : 3$

Solution:

$\text{Let } m = 5 \text{ kg, } F = 10 \text{ N, } g = 10 \text{ ms}^{-2}.$ $\text{During ascent, net force } = mg + F = 5 \times 10 + 10 = 60 \text{ N}$ $\text{During descent, net force } = mg - F = 5 \times 10 - 10 = 40 \text{ N}$ $\text{Ratio of time of ascent to descent} = \frac{\text{Force during descent}}{\text{Force during ascent}} = \frac{40}{60} = \frac{2}{3}$

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
}