Import Question JSON

Current Question (ID: 19006)

Question:

$\text{To find the spring constant (k) of a spring experimentally, a student commits } 2\% \text{ positive error in the measurement of time and } 1\% \text{ negative error in the measurement of mass. The percentage error in determining the value of } k \text{ is:}$

Options:

1. $3\%$
2. $4\%$
3. $5\%$
4. $1\%$

Solution:

$\text{The spring constant } k \text{ is given by } k = \frac{4\pi^2 m}{T^2}$. $\text{The percentage error in } k \text{ is given by:}$ $\Delta k = \left( \frac{\Delta m}{m} + 2 \frac{\Delta T}{T} \right) \times 100\%$. $\text{Given } \Delta m = -1\% \text{ and } \Delta T = 2\%$, $\Delta k = \left( -1 + 2 \times 2 \right) \% = 3\%$.

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
}