Import Question JSON

Current Question (ID: 9827)

Question:

$\text{The minimum work done in pulling up a block of wood weighing 2 kN for a length of 10 m on a smooth plane inclined at an angle of 15° with the horizontal is (given: sin15° = 0.2588):}$

Options:

1. $4.36 \text{ kJ}$
2. $5.17 \text{ kJ}$
3. $8.91 \text{ kJ}$
4. $9.82 \text{ kJ}$

Solution:

$\text{Hint: Work done = Change in potential energy of block. (figure as shown below)}$ $W = mgh$ $\text{Step 1: Find the work done in pulling up a block of wood is given by}$ $\text{Work done = Change in potential energy of block}$ $W = mgh \text{, here height } h = sin\theta$ $\text{Step 2: Weight of block = } mg = 2\text{kN}$ $\text{displacement } d = 10$ $\text{work done } W = mg\sin\theta \times s$ $= 2 \times 10^3 \times \sin15 \times 10$ $= 5.17\text{kJ}$

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
}