Import Question JSON

Current Question (ID: 19037)

Question:

$\text{A particle is moving in a straight line such that its velocity is increasing at } 5 \text{ ms}^{-1} \text{ per meter.}$ $\text{The acceleration of the particle at a point where its velocity is } 20 \text{ ms}^{-1}, \text{ is:}$

Options:

1. $100 \text{ ms}^{-2}$
2. $200 \text{ ms}^{-2}$
3. $300 \text{ ms}^{-2}$
4. $400 \text{ ms}^{-2}$

Solution:

$\text{Hint: } a = v \frac{dv}{dx}$ $\text{Step: Find the acceleration of the particle.}$ $\text{The velocity of the particle is increasing at } 5 \text{ m/s per meter i.e.,}$ $\frac{dv}{dx} = 5 \text{ m/s}$ $\text{The acceleration of the particle is given by;}$ $a = v \frac{dv}{dx}$ $\Rightarrow a = 20 \times 5 = 100 \text{ m/s}^2 \quad [v = 20 \text{ m/s}]$ $\text{Hence, option (1) is the correct answer.}$

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
}