Import Question JSON

Current Question (ID: 10445)

Question:

$\text{The reading of a spring balance when a block is suspended from it in the air is 60 N. This reading is changed to 40 N when the block is submerged in water. The specific gravity of the block, therefore, must be:}$

Options:

1. $3$
2. $2$
3. $6$
4. $\frac{3}{2}$

Solution:

$\text{Let m be the mass of the block.}$ $W = 60 \text{ N}$ $\Rightarrow mg = \rho_b \times V \times g = 60 \ldots\ldots\ldots (1)$ $\text{When the block is submerged in water,}$ $(\rho_b - \rho_w)V \times g = 40 \ldots\ldots\ldots (2)$ $\text{From (1) and (2), we get,}$ $\Rightarrow \frac{\rho_b - \rho_w}{\rho_b} = \frac{2}{3}$ $\Rightarrow \rho_b = 3\rho_w$ $\Rightarrow \frac{\rho_b}{\rho_w} = 3$

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
}