Import Question JSON

Current Question (ID: 19578)

Question:

$\text{In an experiment to verify Stokes's law, a small spherical ball of radius } r \text{ and density } \rho \text{ falls under gravity through a distance } h \text{ in air before entering a tank of water.}$ $\text{If the terminal velocity of the ball inside water is the same as its velocity just before entering the water surface, then the value of } h \text{ is proportional to: (Ignore viscosity of air)}$

Options:

1. $r$
2. $r^4$
3. $r^3$
4. $r^2$

Solution:

$\text{Hint: Velocity after falling } h = \text{ terminal velocity}$ $\text{Step 1: Find the speed of the ball just before entering the water}$ $v = 0$ $mgh = \frac{1}{2} mv^2$ $v = \sqrt{2gh}$ $\text{Step 2: Equate speed } v \text{ with terminal velocity in water}$ $V = V_T = \frac{2r^2g}{9\eta}(\sigma - \rho)$ $\sqrt{h} \propto r^2$

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
}