Import Question JSON

Current Question (ID: 9647)

Question:

$\text{A car moves on a circular path such that its speed is given by } v = Kt, \text{ where } K = \text{constant and } t \text{ is time. Also given radius of the circular path is } r. \text{ The net acceleration of the car at time } t \text{ will be:}$

Options:

1. $\sqrt{K^2 + \left(\frac{K^2t^2}{r}\right)^2}$
2. $2K$
3. $K$
4. $\sqrt{K^2 + K^2t^2}$

Solution:

\text{Hint: } a_{\text{net}} = \sqrt{a_t^2 + a_r^2} \text{Step: Find the net acceleration of the car at time } t. \text{Given: } v = kt \text{The tangential acceleration: } a_t = \frac{dv}{dt} = k \text{The radial acceleration: } a_r = \frac{v^2}{r} = \frac{k^2t^2}{r} \text{The net acceleration of the car is given by: } a_{\text{net}} = \sqrt{a_t^2 + a_r^2} a_{\text{net}} = \sqrt{k^2 + \left(\frac{k^2t^2}{r}\right)^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
}