Import Question JSON

Current Question (ID: 10456)

Question:

A cube floats both in water and in a liquid of specific gravity of $0.8$. Therefore,

Options:

1. (a) and (c) both are correct.
2. only (d) is correct.
3. (a) and (b) both are correct.
4. (a), (b), and (c) are correct.

Solution:

Hint: The apparent weight of a floating object is zero. Step: Analyze each option one by one. (a) The apparent weight of the cube is zero in both water and liquid. Therefore the apparent weight of the cube is the same in water and in liquid. (b) The buoyancy force acting on the cube is the same in water and liquid. The cube will displace an equal volume of water and liquid while floating. (c) The apparent weight of the cube is zero in both water and liquid. Therefore the cube has displaced an equal weight of water and liquid while floating. (d) The buoyancy force exerted by water is greater than the buoyancy force exerted by the liquid, therefore in the case of water more weights are required to be placed on the top surface of the cube to make it just sink. (a) and (c) are correct.

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
}