Import Question JSON

Current Question (ID: 10518)

Question:

The value of g at a place decreases by 2%. Then, the barometric height of mercury:

Options:

1. increases by 2%.
2. decreases by 2%.
3. $\text{remains unchanged.}$
4. $\text{sometimes increases and sometimes decreases.}$

Solution:

\text{Given formula: } h = \frac{P}{\rho g} \text{Therefore: } h \propto \frac{1}{g} \text{ (where P and } \rho \text{ are constant)} \text{If g decreases by 2%, then: } g' = g(1 - 0.02) = 0.98g \text{New height: } h' = \frac{P}{\rho g'} = \frac{P}{\rho \times 0.98g} = \frac{h}{0.98} \text{Percentage increase: } \frac{h' - h}{h} \times 100\% = \left(\frac{1}{0.98} - 1\right) \times 100\% \approx 2.04\%

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
}