Import Question JSON

Current Question (ID: 8828)

Question:

$\text{If in one-dimensional motion, instantaneous speed } v \text{ satisfies } 0 \leq v < v_0, \text{ then:}$

Options:

1. $\text{the displacement in time } T \text{ must always take non-negative values.}$
2. $\text{the displacement } x \text{ in time } T \text{ satisfies } -v_0T < x < v_0T.$
3. $\text{the acceleration is always a non-negative number.}$
4. $\text{the motion has no turning points.}$

Solution:

$\text{Hint: The velocity and displacement are vector quantities.}$ $\text{Step 1: Find the maximum value of the velocity in two directions.}$ $\text{For maximum and minimum displacement, we have to keep in mind the magnitude and direction of maximum velocity.}$ $\text{As maximum velocity in the positive direction is } v_0 \text{ maximum velocity in opposite direction is also } v_0.$ $\text{Step 2: Find the maximum and minimum displacement.}$ $\text{Maximum displacement in one direction = } v_0T$ $\text{Maximum displacement in opposite directions = } -v_0T$ $\text{Hence, } -v_0T < x < v_0T$ $\text{Hence, option (2) is the correct answer.}$

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
}