Import Question JSON

Current Question (ID: 9597)

Question:

$\text{The time taken by a block of wood (initially at rest) to slide down a smooth inclined plane 9.8 m long (angle of inclination is 30°) is:}$

Options:

1. $\frac{1}{2} \text{ sec}$
2. $2 \text{ sec}$
3. $4 \text{ sec}$
4. $1 \text{ sec}$

Solution:

$\text{Hint: Use acceleration along the plane.}$ $\text{Step: Find the time taken by a block of wood to slide down a smooth inclined plane.}$ $\text{Given: } u = 0, a = g\sin 30°$ $\text{For one-dimensional motion along a plane,}$ $s = ut + \frac{1}{2}at^2 \Rightarrow 9.8 = 0 + \frac{1}{2} \times g\sin 30° \times t^2$ $\Rightarrow t = 2 \text{ s}$ $\text{Therefore, the time taken by a block of wood to slide down a smooth inclined plane is 2 s.}$ $\text{Hence, option (2) is the correct answer.}$

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
}