Import Question JSON

Current Question (ID: 9912)

Question:

$\text{A block of mass m is moving with speed v towards a spring block system. If the collision is perfectly inelastic, then the maximum compression in the spring will be:}$

Options:

1. $v\sqrt{\frac{m}{k}}$
2. $v\sqrt{\frac{2m}{k}}$
3. $mv\sqrt{\frac{v}{2k}}$
4. $v\sqrt{\frac{m}{2k}}$

Solution:

$\text{1. Collision: } m_1v_1 = (m_1 + m_2)V_{final}$ $mv = (m + m)V_{final} \Rightarrow V_{final} = v/2$ $\text{2. Spring Compression: } \frac{1}{2}(m_1 + m_2)V_{final}^2 = \frac{1}{2}kx^2$ $\frac{1}{2}(2m)(v/2)^2 = \frac{1}{2}kx^2$ $m(v^2/4) = kx^2/2$ $mv^2/4 = kx^2/2$ $x^2 = \frac{mv^2}{2k}$ $x = v\sqrt{\frac{m}{2k}}$ $\text{The final answer is } \boxed{4}$

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
}