Import Question JSON

Current Question (ID: 9796)

Question:

$\text{A roller coaster is designed such that riders experience "weightlessness" as they go round the top of a hill whose radius of curvature is 20 m. The speed of the car at the top of the hill is between:}$

Options:

1. $14 \text{ m/s and } 15 \text{ m/s}$
2. $15 \text{ m/s and } 16 \text{ m/s}$
3. $16 \text{ m/s and } 17 \text{ m/s}$
4. $13 \text{ m/s and } 14 \text{ m/s}$

Solution:

$\text{Hint: At the topmost point, the normal reaction is zero.}$ $\text{Step 1: Balance the vertical forces.}$ $Mg - N = \frac{Mv^2}{r}$ $\text{Step 2: Use the condition of weightlessness.}$ $\text{For weightlessness, } N = 0$ $\text{So, } \frac{Mv^2}{r} = Mg$ $\text{Or } v^2 = gr$ $\text{Or } v = \sqrt{gr}$ $\text{Step 3: Put the given values.}$ $\text{Given, } r = 20\text{m and } g = 10 \text{ m/s}^2$ $\text{By putting the values,}$ $v = 14.14 \text{ m/s}$ $\text{So, it will be between 14 m/s and 15 m/s.}$

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
}