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Current Question (ID: 10532)

Question:

$\text{A spherical ball of radius } r \text{ is falling in a viscous fluid of viscosity } \eta \text{ with a velocity } v. \text{ The retarding viscous force acting on the spherical ball is:}$

Options:

1. $\text{inversely proportional to } r \text{ but directly proportional to velocity } v.$
2. $\text{directly proportional to both radius } r \text{ and velocity } v.$
3. $\text{inversely proportional to both radius } r \text{ and velocity } v.$
4. $\text{directly proportional to } r \text{ but inversely proportional to } v.$

Solution:

$\text{According to Stokes' law, the viscous force acting on a spherical object moving through a viscous fluid is given by:}$ $F = 6\pi\eta rv$ $\text{From this formula, we can see that:}$ $\text{- The force is directly proportional to the radius } r$ $\text{- The force is directly proportional to the velocity } v$ $\text{- The force is also directly proportional to the viscosity } \eta$ $\text{Therefore, the viscous force is directly proportional to both radius } r \text{ and velocity } v.$

Import JSON File

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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
}