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Current Question (ID: 10515)

Question:

$\text{A liquid is poured into three vessels of the same base area and equal heights as shown in the figure, then:}$

Options:

1. $\text{The maximum force on the base will be for the vessel } C\text{.}$
2. $\text{The maximum force on the base will be for the vessel } B\text{.}$
3. $\text{The maximum force on the base will be for the vessel } A\text{.}$
4. $\text{Force on the base will be equal for all the vessels.}$

Solution:

$\text{Hint: } A_1 v_1 = A_2 v_2$ $\text{The force on the base of a vessel depends on the hydrostatic pressure, which is given by } F = \rho g h A$ $\text{where } \rho \text{ is the density of liquid, } g \text{ is acceleration due to gravity, } h \text{ is the height of liquid column, and } A \text{ is the base area.}$ $\text{Since all three vessels have the same base area and equal heights of liquid, the force on the base will be equal for all vessels.}$ $\text{The shape of the vessel does not affect the hydrostatic pressure at the base, only the height of the liquid column matters.}$

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
}