Import Question JSON

Current Question (ID: 9671)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): Uniform circular motion is the only example of a situation in which the speed of a particle remains constant even though a force is acting on the particle.}$ $\text{Reason (R): In uniform circular motion, a force acting along the circle pushes the particle forward.}$

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. $\text{Both (A) and (R) are False.}$

Solution:

$\text{Hint: In a uniform circular motion, a force acts along radially.}$ $\text{Analysis of Assertion (A):}$ $\text{Assertion (A) is FALSE. Uniform circular motion is NOT the only example where speed remains constant while a force acts on the particle. There are other examples like motion in a straight line with zero net force, or motion under conservative forces where kinetic energy is conserved.}$ $\text{Analysis of Reason (R):}$ $\text{Reason (R) is FALSE. In uniform circular motion, the force acts radially (towards the center), not along the circle. The centripetal force is always directed toward the center of the circle, perpendicular to the velocity.}$ $\text{Since both (A) and (R) are false, the correct answer is option 4.}$

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
}