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Current Question (ID: 9829)

Question:

$\text{A block of mass m is placed in an elevator moving down with an acceleration } \frac{g}{3}\text{. The work done by the normal reaction on the block as the elevator moves down through a height h is:}$

Options:

1. $\frac{-2mgh}{3}$
2. $\frac{-mgh}{3}$
3. $\frac{2mgh}{3}$
4. $\frac{mgh}{3}$

Solution:

$\text{When a block is placed in an elevator moving down with an acceleration of g/3, the normal reaction exerted by the elevator on the block does work as the elevator moves down through a height h. The work done by the normal reaction can be calculated using the formula:}$ $\text{Work = Force × Distance}$ $\text{In this case, the force is the normal reaction exerted by the elevator, and the distance is the height h. The normal reaction force is equal to the weight of the block, which is mg, where m is the mass of the block. Therefore, the work done by the normal reaction is:}$ $\text{Work = mg × h}$ $\text{Substituting the given value of acceleration, g/3, we find:}$ $\text{Work = (mg/3) × h}$ $\text{The correct option is (B) -mgh/3.}$

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
}