Import Question JSON

Current Question (ID: 20026)

Question:

$\text{A small point mass carrying a positive charge is released from the edge of a table.}$ $\text{There is a uniform electric field in the horizontal direction.}$ $\text{Which of the following options correctly describes the trajectory of the mass?}$ $\text{(The curves are drawn schematically and are not to scale).}$

Options:

1. $\text{Option 1: Concave down curve}$
2. $\text{Option 2: Concave up curve}$
3. $\text{Option 3: Concave up curve}$
4. $\text{Option 4: Straight line}$

Solution:

$\text{Hint: The particle will move in a straight line.}$ $\text{Step: Find the correct graph for the motion of the particle.}$ $\text{As the particle is released from rest then the initial velocity of the particle is zero i.e., } u = 0$ $\text{Two forces are acting on the charged particle, } qE \text{ along } x\text{-axis}$ $\text{and } mg \text{ along } y\text{-axis as shown in the figure.}$ $\text{The distance in } y \text{ direction is given by; } y = \frac{1}{2}gt^2 \ldots (1)$ $\text{The distance in } x \text{ direction is given by; } x = \frac{1}{2} \frac{qE}{m} t^2 \ldots (2)$ $\text{By dividing the equation (1) by equation (2) we get;}$ $\frac{y}{x} = \frac{mg}{qE}$ $\Rightarrow y = \frac{mg}{qE} x \ldots (3)$ $\text{The equation (3) represents a straight line with slope } \frac{mg}{qE}. $ $\text{Therefore, the correct graph for the motion of the particle is given in the figure below;}$ $\text{Hence, option (4) is the correct answer.}$

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
}