Import Question JSON

Current Question (ID: 12053)

Question:

The maximum static friction on a body is $F=\mu N$. Here, $N=\text{normal reaction force on the body}$, $\mu=\text{coefficient of static friction}$. The dimensions of $\mu$ are

Options:

1. $[MLT^{-2}]$
2. $[M^0L^0T^0\theta^{-1}]$
3. Dimensionless
4. None of these

Solution:

Given the equation for static friction, $F=\mu N$. We can find the dimensions of $\mu$ by rearranging the formula to $\mu = \frac{F}{N}$. Since both $F$ (force) and $N$ (normal reaction force) have the same dimensions, $[MLT^{-2}]$, their ratio is dimensionless. Therefore, $\mu$ is dimensionless. $[\mu] = [\frac{F}{N}] = \frac{[MLT^{-2}]}{[MLT^{-2}]} = [M^0L^0T^0]$.

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
}