Import Question JSON

Current Question (ID: 10441)

Question:

$\text{If two iron balls when fully immersed in water experience thrust force in the ratio of } 1 : 2, \text{ then the ratio of the masses of the balls will be:}$

Options:

1. $1 : 1$
2. $1 : 2$
3. $2 : 1$
4. $1 : 4$

Solution:

\text{Hint: Upthrust is directly proportional to the volume of displaced water.} \text{Step 1: Find the volume in terms of mass.} \text{Volume of a body is given by: } V = \frac{m}{\rho} \text{So, } V_1 = \frac{m_1}{\rho} \text{ and } V_2 = \frac{m_2}{\rho} \text{Step 2: Find thrust force on the objects.} F_B = \rho_w \times V \times g F_1 = \rho_w \times V_1 \times g F_2 = \rho_w \times V_2 \times g \frac{F_1}{F_2} = \frac{V_1}{V_2} = \frac{m_1}{m_2} \text{Therefore: } \frac{m_1}{m_2} = \frac{1}{2} \text{Note: The upthrust depends on the volume of the liquid displaced not the mass of the body being immersed in the liquid.}

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
}