Import Question JSON

Current Question (ID: 9840)

Question:

$\text{When a body moves non-uniformly on a circular path:}$

Options:

1. $\text{no work is done by the tangential force.}$
2. $\text{no work is done by the centripetal force.}$
3. $\text{work done by the tangential force is always positive.}$
4. $\text{work done by the centripetal force is negative.}$

Solution:

$\text{Hint: Work done by the centripetal force is zero.}$ $\text{Step 1: As centripetal force is perpendicular to the velocity so the power supply or work done by the centripetal force is zero.}$ $\text{The diagram shows a circular path with velocity } v \text{ tangential to the circle, tangential acceleration } a_T \text{ in the direction of velocity, and radial acceleration } a_r \text{ pointing toward the center.}$ $\text{Power is given by } P = \vec{F} \cdot \vec{v}$ $\text{For radial force: } P_R = 0 \text{ (since radial force is perpendicular to velocity)}$ $\text{Step 2: Power supply (work done) by tangential force}$ $P_T = \vec{F} \cdot \vec{v}$ $\text{As it is not specified that tangential force is accelerating or retarding, so we can't say that work done by the tangential force is positive or negative.}$

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
}