Import Question JSON

Current Question (ID: 18913)

Question:

$\text{In a simple pendulum experiment for determination of acceleration due to gravity } (g), \text{ time taken for } 20 \text{ oscillations is measured by using a watch of } 1 \text{ second least count.}$ $\text{The mean value of time taken comes out to be } 30 \text{ s.}$ $\text{The length of pendulum is measured by using a meter scale of least count } 1 \text{ mm and the value obtained is } 55.0 \text{ cm.}$ $\text{The percentage error in the determination of } g \text{ is close to:}$

Options:

1. $0.7\%$
2. $6.8\%$
3. $0.2\%$
4. $3.5\%$

Solution:

$\text{Hint: } T = 2\pi \sqrt{\frac{l}{g}}$ $T = 2\pi \sqrt{\frac{l}{g}}$ $g = \frac{4\pi^2 l}{T^2}$ $\left| \frac{\Delta g}{g} \right| = \left| \frac{\Delta l}{l} \right| + 2 \left| \frac{\Delta T}{T} \right|$ $\% \left| \frac{\Delta g}{g} \right| = \left( \frac{0.1}{55} \right) \times 100 + 2 \left( \frac{1}{30} \right) \times 100$ $= 6.8\%$

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
}