Import Question JSON

Current Question (ID: 16420)

Question:

$\text{A charged particle } q \text{ of mass } m \text{ is released on the } y\text{-axis at } y = a \text{ in an}$ $\text{electric field } \vec{E} = -4y\hat{j}. \text{ The speed of the particle on reaching the origin will be:}$

Options:

1. $\sqrt{\frac{2a}{mq}}$
2. $\sqrt{\frac{a}{mq}}$
3. $2a\sqrt{\frac{q}{m}}$
4. $2\sqrt{\frac{a}{mq}}$

Solution:

$\text{Hint: } \vec{F}_e = q\vec{E}$ $\vec{F}_e = q\vec{E}$ $= -4qy\hat{j}$ $\text{The work done by the electric force is given by:}$ $W_e = \int \vec{F}_e \cdot d\vec{r}$ $W_e = -\int_0^a 4qydy$ $\Rightarrow W_e = 2qa^2$ $\text{Step 2: Find the speed of the particle on reaching the origin}$ $W_e = \Delta K$ $W_e = \frac{1}{2}mv^2 - 0$ $2qa^2 = \frac{1}{2}mv^2$ $\Rightarrow v = 2a\sqrt{\frac{q}{m}}$ $\text{Hence, option (3) is the correct answer.}$

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
}