Import Question JSON

Current Question (ID: 10372)

Question:

The edge of an aluminum cube is $10 \text{ cm}$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100 \text{ kg}$ is then attached to the opposite face of the cube. The shear modulus of aluminum is $25 \text{ GPa}$. What is the vertical deflection of this face?

Options:

1. $4.86 \times 10^{-6} \text{ m}$
2. $3.92 \times 10^{-7} \text{ m}$
3. $3.01 \times 10^{-7} \text{ m}$
4. $6.36 \times 10^{-7} \text{ m}$

Solution:

\text{Hint: Use the formula for shear modulus.} \text{Step: Find the vertical deflection of this face.} \text{We know that the shear modulus is given by; } \eta = \frac{\text{shear stress}}{\text{shear strain}} $\eta = \frac{F \times L}{A \times \Delta L}$ \text{Now, calculate vertical deflection by rearranging the above expression given by; } \eta = \frac{F \times L}{A \times \Delta L} \text{So, the vertical deflection } \Delta L = \frac{m \times g \times L}{A \times \eta} $\Delta L = \frac{100 \times 9.8 \times 0.1}{0.1 \times 0.1 \times 25 \times (10)^9}$ $\Delta L = 3.92 \times 10^{-7} \text{ m}$ \text{Hence, option (2) 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
}