Import Question JSON

Current Question (ID: 19250)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A):}$ \text{Body 'P' having mass } M \text{ moving with speed } 'u' \text{ has head-on collision elastically with another body 'Q' having mass } 'm' \text{ initially at rest. If } m \ll M, \text{ body 'Q' will have a maximum speed equal to } '2u' \text{ after collision.}$ $\text{Reason (R):}$ \text{During elastic collision, the momentum and kinetic energy are both conserved.}$

Options:

1. $\text{Both (A) and (R) are true and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are true but (R) is not the correct explanation of (A).}$
3. $\text{(A) is true but (R) is false.}$
4. $\text{(A) is false but (R) is true.}$

Solution:

$\text{Hint: Momentum is conserved in all collisions.}$ $\text{For } e = 1 \text{ and second body at rest}$ $\text{V}_2 = \frac{2 m_1 u_1}{m_1 + m_2} = \frac{2u(M)}{M+m} \simeq 2u$ $\text{Since } M \gg m$

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
}