Import Question JSON

Current Question (ID: 19011)

Question:

$\text{Young's modulus is determined by the equation given by}$ $Y = 49000 \frac{m}{l} \frac{\text{dyne}}{\text{cm}^2}$ $\text{where M is the mass and I is the extension of wire used in the experiment.}$ $\text{Now error in Young modules (Y) is estimated by taking data from M I plot in graph paper.}$ $\text{The smallest scale divisions are 5 g and 0.02 cm along load axis and extension axis respectively.}$ $\text{If the value of M and I are 500 g and 2 cm respectively then percentage error of Y is:}$

Options:

1. $0.2\%$
2. $0.02\%$
3. $2\%$
4. $0.5\%$

Solution:

$\text{Percentage error in Y is given by:}$ $\frac{\Delta Y}{Y} \times 100 = \frac{\Delta M}{M} \times 100 + \frac{\Delta I}{I} \times 100$ $\text{Given:}$ $\Delta M = 5 \text{ g}, \Delta I = 0.02 \text{ cm}, M = 500 \text{ g}, I = 2 \text{ cm}$ $\frac{\Delta M}{M} \times 100 = \frac{5}{500} \times 100 = 1\%$ $\frac{\Delta I}{I} \times 100 = \frac{0.02}{2} \times 100 = 1\%$ $\text{Total percentage error in Y} = 1\% + 1\% = 2\%$

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
}