Import Question JSON

Current Question (ID: 9596)

Question:

$\text{A body sliding on a smooth inclined plane requires 4 seconds to reach the bottom starting from the rest at the top. How much time does it take to cover one-fourth distance starting from the rest at the top?}$

Options:

1. $1 \text{ s}$
2. $2 \text{ s}$
3. $4 \text{ s}$
4. $16 \text{ s}$

Solution:

\text{Hint: } s = ut + \frac{1}{2}at^2 \text{Step: Find the time taken by the body to cover one-fourth distance starting from rest.} \text{Since the body starts from rest, initial velocity } u = 0 \text{Using the equation of motion:} S = ut + \frac{1}{2}at^2 = 0 + \frac{1}{2}at^2 = \frac{1}{2}at^2 \text{From this equation, we can see that } t \propto \sqrt{S} \text{This means that time is proportional to the square root of distance.} \text{If the distance becomes one-fourth, then:} \frac{t_2}{t_1} = \sqrt{\frac{S_2}{S_1}} = \sqrt{\frac{S/4}{S}} = \sqrt{\frac{1}{4}} = \frac{1}{2} \text{Given that } t_1 = 4 \text{ s for the full distance} \text{Therefore: } t_2 = \frac{t_1}{2} = \frac{4}{2} = 2 \text{ 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
}