Import Question JSON

Current Question (ID: 10494)

Question:

$\text{An iron sphere is dropped into a viscous liquid. Which of the following represents its acceleration } (a) \text{ versus time } (t) \text{ graph?}$

Options:

1. $\text{Graph showing acceleration starting from zero and increasing asymptotically to a constant value}$
2. $\text{Graph showing acceleration increasing linearly with time}$
3. $\text{Graph showing acceleration starting from maximum value and decreasing exponentially to zero}$
4. $\text{Graph showing acceleration starting from maximum value and decreasing exponentially, approaching zero asymptotically}$

Solution:

$\text{As the velocity of the sphere increases inside the liquid, the viscous force also increases as it is directly proportional to the velocity of the body. After some time, the velocity of the sphere becomes constant and the viscous force balances the gravitational force. So, the acceleration of the sphere decreases with time and becomes zero when the body achieves terminal velocity.}$ $\text{Initially, when the sphere is dropped, it has maximum acceleration equal to } g. \text{ As it gains velocity, the viscous drag increases, reducing the net downward force and thus the acceleration. Eventually, when terminal velocity is reached, the acceleration becomes zero.}$ $\text{The correct graph shows acceleration starting from maximum value and decreasing exponentially, approaching zero asymptotically.}$

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
}