Import Question JSON

Current Question (ID: 10435)

Question:

$\text{A triangular lamina of area A and height h is immersed in a liquid of density } \rho \text{ in a vertical plane with its base on the surface of the liquid. The thrust on the lamina is:}$

Options:

1. $\frac{1}{2}A\rho gh$
2. $\frac{1}{3}A\rho gh$
3. $\frac{1}{6}A\rho gh$
4. $\frac{2}{3}A\rho gh$

Solution:

$\text{The position of the centroid from the surface of the liquid = } \frac{h}{3}$ $\text{Thrust on lamina = pressure at centroid × Area of the lamina}$ $= \frac{h\rho g}{3} \times A = \frac{1}{3}A\rho gh$ $\text{As the area of the lamina is variable with the depth, so we will calculate the pressure at the centroid to find the effective force on the lamina.}$

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
}