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Current Question (ID: 8883)

Question:

$\text{A balloon starts from the ground from rest with an upward acceleration of } 2 \text{ m/s}^2. \text{ After 1 sec, a stone is dropped from it. The time taken by the stone to strike the ground is approximately:}$

Options:

1. $0.3 \text{ s}$
2. $0.7 \text{ s}$
3. $1 \text{ s}$
4. $1.4 \text{ s}$

Solution:

\text{Hint: } s = ut + \frac{1}{2}at^2 \text{Step: Find the time taken by the stone to strike the ground.} \text{After 1 second, the velocity of the balloon:} v = 0 + 2 \times 1 = 2 \text{ m/s} \text{and height of the balloon: } h = \frac{1}{2} \times 2 \times (1)^2 = 1 \text{ m} \text{For the stone: } u = +2 \text{ m/s and } h = -1 \text{ m} \text{Now, using the second equation of motion:} -1 = 2 \times t - \frac{1}{2}gt^2 \text{Substituting } g = 10 \text{ m/s}^2\text{:} -1 = 2t - \frac{1}{2} \times 10 \times t^2 \text{Simplifying:} -1 = 2t - 5t^2 \text{Rearranging:} 5t^2 - 2t - 1 = 0 \text{Using quadratic formula:} t = \frac{2 \pm \sqrt{4 + 4 \times 5}}{10} = \frac{2 \pm \sqrt{24}}{10} = 0.7\text{ s} \text{Therefore, the time taken by the stone to strike the ground is 0.7 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
}