Import Question JSON

Current Question (ID: 19309)

Question:

$\text{A body of } m \text{ kg slides from rest along the curve of vertical circle from point A to B in frictionless path. The velocity of the body at B is –}$ $\text{(given, } R = 14 \text{ m, } g = 10 \text{ m/s}^2 \text{ and } \sqrt{2} = 1.4)}$

Options:

1. $21.9 \text{ m/s}$
2. $10.6 \text{ m/s}$
3. $19.8 \text{ m/s}$
4. $16.7 \text{ m/s}$

Solution:

$\text{Using conservation of energy:}$ $mgh = \frac{1}{2}mv^2$ $\Rightarrow v = \sqrt{2gh}$ $\text{At point B, } h = R(1 - \cos 45^\circ)$ $\Rightarrow h = 14(1 - \frac{1}{\sqrt{2}})$ $\Rightarrow v = \sqrt{2 \times 10 \times 14(1 - \frac{1}{1.4})}$ $\Rightarrow v = 21.9 \text{ m/s}$

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
}