Import Question JSON

Current Question (ID: 10338)

Question:

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:

$\text{Assertion (A): If the ice on the polar caps of the earth melts, then the length of the day will increase.}$ $\text{Reason (R): Moment of inertia of the earth increases, as ice on polar caps melts.}$ $\text{Analysis of Reason (R):}$ $\text{When polar ice melts, water redistributes from the poles (near Earth's rotation axis) toward the equatorial regions (farther from the axis). Since moment of inertia } I = \sum mr^2 \text{, moving mass from smaller radius to larger radius increases the moment of inertia. Therefore, Reason (R) is TRUE.}$ $\text{Analysis of Assertion (A):}$ $\text{By conservation of angular momentum: } L = I\omega = \text{constant}$ $\text{When } I \text{ increases, } \omega \text{ (angular velocity) must decrease to maintain constant angular momentum.}$ $\text{Since day length } = \frac{2\pi}{\omega} \text{, a decrease in } \omega \text{ results in an increase in day length. Therefore, Assertion (A) is TRUE.}$ $\text{Relationship between A and R:}$ $\text{Reason (R) directly explains why Assertion (A) is true. The increase in Earth's moment of inertia due to melting ice is the direct cause for the decrease in angular speed and thus the increase in the length of the day, based on the conservation of angular momentum.}$

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
}