Import Question JSON

Current Question (ID: 8925)

Question:

$\text{An elevator whose floor-to-ceiling height is 12 meters, moves upward with an acceleration of 2.2 m/s}^2\text{. After 1.5 s since starting, a bolt falls from its ceiling. The time taken by the bolt to reach the floor is:}$

Options:

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

Solution:

$\text{Hint: } \vec{a}_{B,L} = \vec{a}_B - \vec{a}_L$ $\text{Step 1: Calculate the acceleration of the ball in the lift frame.}$ $\text{The motion of the ball in the lift frame is shown in the figure below;}$ $\text{The acceleration of the ball in the lift frame is given by;}$ $\vec{a}_{B,L} = \vec{a}_B - \vec{a}_L$ $\Rightarrow a_{B,L} = 9.8 - (-2.2) = 12 \text{ m/s}^2$ $\text{Step 2: Calculate the time taken by the ball to reach the floor.}$ $\text{The initial velocity of the ball with respect to lift is zero.}$ $s = \frac{1}{2}at^2$ $\Rightarrow 12 = \frac{1}{2} \times 12t^2$ $\Rightarrow t^2 = 2$ $\Rightarrow t = \sqrt{2} \text{ s}$ $\text{Hence, option (3) is the correct answer.}$

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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
}