Import Question JSON

Current Question (ID: 9599)

Question:

$\text{A particle starts from the origin at } t = 0 \text{ sec with a velocity of } 10\hat{j} \text{ m/s and moves in the } x-y \text{ plane with a constant acceleration of } (8.0\hat{i} + 2.0\hat{j}) \text{ m/s}^2\text{. At what time is the } x\text{-coordinate of the particle 16 m?}$

Options:

1. $2 \text{ s}$
2. $3 \text{ s}$
3. $4 \text{ s}$
4. $1 \text{ s}$

Solution:

$\text{Hint: Use the equations of motion to find the position vector.}$ $\text{Step: Find the x-coordinate of the position vector.}$ $\text{Initial velocity} = 10\hat{j}$ $\text{Initial x-component of velocity} = 0$ $\text{Acceleration in x-component} = 8 \text{ ms}^{-2}$ $S_x = u_x t + \frac{1}{2}a_x t^2$ $S_x = 16 \text{ m}$ $u_x = 0$ $a_x = 8 \text{ ms}^{-2}$ $\Rightarrow 16 = (0)t + \frac{1}{2}(8)t^2$ $t^2 = 4$ $t = 2$ $\text{Hence, option (1) is the correct answer.}$

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
}