Import Question JSON

Current Question (ID: 10499)

Question:

$\text{An air bubble of radius } r \text{ in water is at a certain depth below the water surface. If } P \text{ is the pressure inside the bubble, then the depth below the water surface is:}$ $\text{(}P_0 = \text{atmospheric pressure, } \rho = \text{density of water, } T = \text{surface tension of water)}$

Options:

1. $\frac{P - P_0}{\rho g} - \frac{4T}{r\rho g}$
2. $\frac{P + P_0}{\rho g} + \frac{2T}{r\rho g}$
3. $\frac{P - P_0}{\rho g} - \frac{2T}{r\rho g}$
4. $\frac{P - P_0}{\rho g} + \frac{2T}{2r\rho g}$

Solution:

\text{The pressure just outside the bubble } = P_0 + h\rho g \text{The pressure inside the bubble, } P = P_0 + h\rho g + \frac{2T}{r} \Rightarrow h\rho g = P - P_0 - \frac{2T}{r} \Rightarrow h = \frac{P - P_0}{\rho g} - \frac{2T}{r\rho g}

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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
}