Import Question JSON

Current Question (ID: 10345)

Question:

$\text{A uniform wire of length 3 m and mass 10 kg is suspended vertically from one end and loaded at another end by a block of mass 10 kg. The radius of the cross-section of the wire is 0.1 m. The stress in the middle of the wire is: (Take } g = 10 \text{ ms}^{-2}\text{)}$

Options:

1. $1.4 \times 10^4 \text{ N/m}^2$
2. $4.8 \times 10^3 \text{ N/m}^2$
3. $96 \times 10^4 \text{ N/m}^2$
4. $3.5 \times 10^3 \text{ N/m}^2$

Solution:

\text{Hint: Total force = W_block + W_wire} \text{Step 1: Draw the diagram.} \text{The wire is suspended vertically with a 10 kg block at the bottom.} \text{At the middle of the wire, we need to find the stress.} \text{Step 2: Find tension in the middle of the wire.} \text{At the middle of the wire, the tension is due to:} \text{- Weight of the block: } 10 \times 10 = 100 \text{ N} \text{- Weight of the lower half of the wire: } 5 \times 10 = 50 \text{ N} \text{Therefore, tension T = 100 + 50 = 150 N} \text{Step 3: Calculate the stress.} \text{Cross-sectional area: } A = \pi r^2 = \pi (0.1)^2 = 0.01\pi \text{ m}^2 \text{Stress = T/A = 150/(0.01}\pi\text{) = 15000/}\pi\text{ = 4.8 × 10}^3\text{ N/m}^2

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
}