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Current Question (ID: 8720)

Question:

$\text{If the dimensions of a physical quantity are given by } [M^a L^b T^c]\text{, then the physical quantity will be:}$

Options:

1. $\text{pressure if } a = 1, b = -1, c = -2$
2. $\text{velocity if } a = 1, b = 0, c = -1$
3. $\text{acceleration if } a = 1, b = 1, c = -2$
4. $\text{force if } a = 0, b = -1, c = -2$

Solution:

$\text{Hint: Recall the dimensions of different quantities.}$ $\text{Step: Find the values of the constants } a, b, c \text{ for different quantities.}$ $(i) \text{Dimensions of velocity} = [M^0 L^1 T^{-1}]$ $\text{Therefore, the values of constants are } a = 0, b = 1 \text{ and } c = -1$ $(ii) \text{Dimensions of acceleration} = [M^0 L^1 T^{-2}]$ $\text{Therefore, the values of constants are } a = 0, b = 1 \text{ and } c = -2$ $(iii) \text{Dimensions of force} = [M^1 L^1 T^{-2}]$ $\text{Therefore, the values of constants are } a = 1, b = 1 \text{ and } c = -2$ $(iv) \text{Dimensions of pressure} = [M^1 L^{-1} T^{-2}]$ $\text{Therefore, the values of constants are } a = 1, b = -1 \text{ and } c = -2$ $\text{Therefore, the physical quantity is pressure.}$ $\text{Hence, option (1) is the correct answer.}$

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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
}