Import Question JSON

Current Question (ID: 18937)

Question:

$\text{A torque meter is calibrated to reference standards of mass, length, and time each with 5\% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of:}$

Options:

1. $15\%$
2. $25\%$
3. $75\%$
4. $5\%$

Solution:

$\text{Hint: } \tau = Fd$ $\text{Step 1: Find the dimensions of torque.}$ $\tau = Fd$ $\Rightarrow \tau = mad$ $\Rightarrow \tau = [M][LT^{-2}][L]$ $\Rightarrow \tau = [ML^2T^{-2}]$ $\text{Step 2: Find the accuracy of torque meter.}$ $\frac{\Delta \tau}{\tau} \times 100 = \frac{\Delta M}{M} \times 100 + 2 \frac{\Delta L}{L} \times 100 + 2 \frac{\Delta T}{T} \times 100$ $\Rightarrow \frac{\Delta \tau}{\tau} \times 100 = 5\% + 10\% + 10\%$ $\Rightarrow \frac{\Delta \tau}{\tau} \times 100 = 25\%$ $\text{Hence, option (2) is the correct answer.}$

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
}