Import Question JSON

Current Question (ID: 8723)

Question:

$\text{Which, among the pairs of quantities has the same dimensions?}$

Options:

1. $\frac{\text{force}}{\text{volume}}\text{, surface tension}$
2. $\text{torque, pressure } \times \text{ volume}$
3. $\text{specific heat } \times \text{ mass, energy}$
4. $\frac{\text{pressure}}{\text{acceleration}}\text{, density}$

Solution:

$\text{Hint: Specific heat, } s = \frac{Q}{m\Delta T} \text{ and torque, } \vec{\tau} = \vec{r} \times \vec{F}$ $\text{Step: Find the dimensions of each pair of quantities.}$ $(1) \frac{Force}{Volume} = [ML^{-2}T^{-2}] \text{ and Surface tension} = \frac{Force}{length} = [MT^{-2}]$ $(2) \text{Torque} = Force \times Distance = [ML^2T^{-2}] \text{ and Pressure} \times \text{volume} = [ML^2T^{-2}]$ $(3) \text{Specific heat} \times \text{mass} = \frac{Q}{m\Delta T} = [L^2T^{-3}] \text{ and energy} = [ML^2T^{-2}]$ $(4) \frac{Pressure}{Acceleration} = [ML^{-2}] \text{ and Density} = [ML^{-3}]$ $\text{Hence the given pairs of quantities, torque, pressure } \times \text{ volume has the same dimensions.}$

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
}