Import Question JSON

Current Question (ID: 8935)

Question:

$\text{An elevator car, whose floor to ceiling distance is equal to 2.7 m, starts ascending with constant acceleration of 1.2 ms}^{-2}\text{. 2 sec after the start, a bolt begins falling from the ceiling of the car. The free fall time of the bolt is:}$

Options:

1. $\sqrt{0.54} \text{ s}$
2. $\sqrt{6} \text{ s}$
3. $0.7 \text{ s}$
4. $1 \text{ s}$

Solution:

$\text{Hint: Recall the concept of relative velocity.}$ $\text{Step: Find the free fall time of the bolt.}$ $\text{Using relative motion concept, } a_{bolt,car} = a_{bolt} - a_{car}$ $= 9.8 - (-1.2) = 11 \text{ m/s}^2$ $\text{Also the initial velocity of the bolt w.r.t car } u = 0$ $t = \sqrt{\frac{2h}{g+a}} = \sqrt{\frac{2 \times 2.7}{9.8+1.2}} = \sqrt{\frac{5.4}{11}} = \sqrt{0.49} = 0.7 \text{ sec}$ $\text{As } u = 0 \text{ and lift is moving upward with acceleration.}$ $\text{Hence, option (3) is the correct answer.}$

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
}