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Current Question (ID: 16528)

Question:

$\text{An electric dipole of moment } \vec{p} \text{ is lying along a uniform electric field } \vec{E}. \text{ The work done in rotating the dipole by } 90^\circ \text{ is:}$

Options:

1. $\sqrt{2}pE$
2. $\frac{pE}{2}$
3. $2pE$
4. $pE$

Solution:

$\text{Hint: } W = pE(\cos \theta_1 - \cos \theta_2)$ $\text{Step: Find the work done in rotating the dipole by } 90^\circ$ $\text{If the dipole is rotated from an angle } \theta_1 \text{ to } \theta_2, \text{ then work done by the external force is given by: } W = pE(\cos \theta_1 - \cos \theta_2)$ $\text{Putting } \theta_1 = 0^\circ, \theta_2 = 90^\circ \ldots (1) \text{ in the Eq. (1), we get}$ $W = pE(\cos 0^\circ - \cos 90^\circ)$ $\Rightarrow W = pE(1 - 0)$ $\Rightarrow W = pE$ $\text{Hence, option (4) is the correct answer.}$

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
}