Import Question JSON

Current Question (ID: 9751)

Question:

$\text{What is the velocity of the block when the angle between the string and the horizontal is } 30^\circ \text{ as shown in the diagram?}$

Options:

1. $v_B = v_P$
2. $v_B = \frac{v_P}{\sqrt{3}}$
3. $v_B = 2v_P$
4. $v_B = \frac{2v_P}{\sqrt{3}}$

Solution:

\text{Hint: applying string constraint.} \text{Step: Apply the string constraint condition} \text{Along the string:} \text{The velocity of the block component along the string direction must equal the velocity of the string.} \text{velocity of the block} = v_B \cos 30° \Rightarrow v_B \cos 30° = v_P \text{Since } \cos 30° = \frac{\sqrt{3}}{2}: v_B \times \frac{\sqrt{3}}{2} = v_P \text{Solving for } v_B: v_B = \frac{v_P}{\cos 30°} = \frac{v_P}{\frac{\sqrt{3}}{2}} = \frac{2v_P}{\sqrt{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
}