Import Question JSON

Current Question (ID: 9601)

Question:

$\text{A body is slipping from an inclined plane of height } h \text{ and length } l\text{. If the angle of inclination is } \theta\text{, the time taken by the body to come from the top to the bottom of this inclined plane is:}$

Options:

1. $\sqrt{\frac{2h}{g}}$
2. $\sqrt{\frac{2l}{g}}$
3. $\frac{1}{\sin \theta}\sqrt{\frac{2h}{g}}$
4. $\sin \theta \sqrt{\frac{2h}{g}}$

Solution:

$\text{Hint: } s = ut + \frac{1}{2}gt^2$ $\text{Step: Find the time taken by the body to come from the top to the bottom of this inclined plane.}$ $\text{Force down the plane} = mg\sin \theta$ $\therefore \text{Acceleration down the plane} = g\sin \theta$ $\text{Since } l = 0 + \frac{1}{2}g\sin \theta t^2$ $\therefore t^2 = \frac{2l}{g\sin \theta} = \frac{2h}{g\sin^2 \theta} \Rightarrow t = \frac{1}{\sin \theta}\sqrt{\frac{2h}{g}}$ $\text{Hence, option (3) is the correct answer.}$

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
}