Import Question JSON

Current Question (ID: 8870)

Question:

$\text{A stone falls freely from rest from a height } h \text{ and it travels a distance of } \frac{9h}{25} \text{ in the last second. The value of } h \text{ is:}$

Options:

1. $145 \text{ m}$
2. $100 \text{ m}$
3. $122.5 \text{ m}$
4. $200 \text{ ms}$

Solution:

\text{Hint: } s = ut + \frac{1}{2}at^2 \text{Step: Find the value of } h\text{.} \text{Distance travelled in } t \text{ seconds:} \text{Here, initial velocity } u = 0 h = \frac{gt^2}{2} \text{ ... (1)} \text{Distance travelled in } n\text{th} \text{ second} = u + \frac{a}{2}(2n-1) \text{Distance travelled in last second} = 0 + \frac{g}{2}(2t-1) = \frac{9h}{25} \text{... (2)} \text{Equating } h \text{ from equation (1) and (2):} \frac{25g(2t-1)}{18} = \frac{gt^2}{2} 9t^2 - 50t + 25 = 0 \text{Solving for } t\text{:} t = \frac{50 \pm \sqrt{2500 - 900}}{18} \text{After solving the above equations we get:} t = \frac{5}{9} \text{ s or } t = 5 \text{ s} \text{Time has to be greater than 1 second, so } t = 5\text{ s} \text{By putting the value of } t \text{ in equation (1): } h = \frac{g(5)^2}{2} = 122.5 \text{ m} \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
}