Import Question JSON

Current Question (ID: 10331)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): If there is no external torque on a body about its centre of mass, then the velocity of the centre of mass remains constant.}$ $\text{Reason (R): The linear momentum of an isolated system remains constant.}$

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:

$\text{Assertion is false, reason is true. If a force is applied at the centre of mass of a rigid body, its torque about centre of mass will be zero but acceleration will be non-zero.}$ $\text{Hence, velocity will change.}$ $\text{The diagram shows a force F applied at the centre of mass C of a body. While the torque about C is zero, the body will still accelerate due to the applied force, causing the velocity of the centre of mass to change.}$ $\text{The reason (R) is true as the linear momentum of an isolated system (no external forces) remains constant according to conservation of momentum.}$ $\text{However, the assertion (A) is false because even with no external torque about the centre of mass, if there is an external force applied at the centre of mass, the velocity will change due to linear acceleration.}$

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
}