Import Question JSON

Current Question (ID: 9863)

Question:

$\text{A bolt of mass 0.3 kg falls from the ceiling of an elevator moving down at a uniform speed of 7 m/s. It hits the floor of the elevator (length of the elevator = 3 m) and does not rebound. What is the heat produced by the impact?}$

Options:

1. $8.82 \text{ J}$
2. $7.65 \text{ J}$
3. $7.01 \text{ J}$
4. $7.98 \text{ J}$

Solution:

$\text{Hint: Heat produced is equal to the change in potential energy.}$ $\text{Mass of the bolt, } m = 0.3 \text{ kg}$ $\text{Speed of the elevator } = 7 \text{ m s}^{-1}$ $\text{Height, } h = 3\text{m}$ $\text{Step 1: Calculate the loss in potential energy.}$ $\text{Loss of P.E. } = mgh$ $\text{Step 2: Find the heat produced.}$ $\text{Since the relative velocity of the bolt with respect to the lift is zero, the potential energy gets converted into heat at the time of impact.}$ $\text{The heat produced = Loss of P.E.}$ $mgh = 0.3 \times 9.8 \times 3 = 8.82 \text{ J}$

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
}