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Current Question (ID: 10289)

Question:

$\text{A force } -F\hat{k} \text{ acts on O, the origin of the coordinate system. The torque at the point (1, -1) will be:}$

Options:

1. $-F(\hat{i} + \hat{j})$
2. $F(\hat{i} + \hat{j})$
3. $-F(\hat{i} - \hat{j})$
4. $F(\hat{i} - \hat{j})$

Solution:

$\text{Given:}$ $\vec{F} = -F\hat{k}$ $\vec{r} = r_o \rightarrow -(\hat{i} - \hat{j}) = -\hat{i} + \hat{j}$ $\text{The torque is calculated using } \vec{\tau} = \vec{r} \times \vec{F}$ $\vec{\tau} = (-\hat{i} + \hat{j}) \times (-F\hat{k})$ $= -F(\hat{i} + \hat{j})$ $\text{Therefore, the torque at point (1, -1) is } -F(\hat{i} + \hat{j})$

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
}