Import Question JSON

Current Question (ID: 10486)

Question:

$\text{The velocity of a small ball of mass m and density } \rho \text{ when dropped in a container filled with glycerin of density } \sigma \text{ becomes constant after sometime. The viscous force acting on the ball in the final stage is:}$

Options:

1. $mg\left(\frac{\sigma}{\rho}\right)$
2. $mg\left(1 + \frac{\sigma}{\rho}\right)$
3. $mg\left(1 - \frac{\sigma}{\rho}\right)$
4. $mg$

Solution:

$\text{At the final stage, } F_{\text{net}} = 0$ $\Rightarrow \text{Weight of the ball} - \text{upthrust} - \text{viscous force} = 0$ $\Rightarrow \text{Viscous force} = mg - V\sigma g$ $= mg - V\rho g \times \frac{\sigma}{\rho}$ $= mg - mg \times \frac{\sigma}{\rho}$ $= mg\left[1 - \frac{\sigma}{\rho}\right]$

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
}