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Current Question (ID: 9816)

Question:

$\text{A body is moving with a velocity of } 2\hat{i} \text{ m/s. If the force acting on the body is } (2\hat{i} + 3\hat{j} + 3\hat{k}) \text{ N, then the momentum of the body is changing in:}$

Options:

1. $X\text{-direction only}$
2. $X\text{-}Y \text{ directions}$
3. $Y\text{-}Z \text{ directions}$
4. $\text{In all } X\text{-}Y\text{-}Z \text{ directions}$

Solution:

\text{Given information:} \text{Initial velocity: } \vec{v} = 2\hat{i} \text{ m/s} \text{Force acting on the body: } \vec{F} = (2\hat{i} + 3\hat{j} + 3\hat{k}) \text{ N} \text{From Newton's second law: } \vec{F} = \frac{d\vec{p}}{dt} \text{where } \vec{p} \text{ is momentum and } \frac{d\vec{p}}{dt} \text{ is the rate of change of momentum.} \text{This means the rate of change of momentum is equal to the applied force.} \text{Since } \vec{F} = (2\hat{i} + 3\hat{j} + 3\hat{k}) \text{ N} \text{We have: } \frac{d\vec{p}}{dt} = (2\hat{i} + 3\hat{j} + 3\hat{k}) \text{This shows that momentum is changing in:} \text{- X-direction with rate } 2 \text{ N} \text{- Y-direction with rate } 3 \text{ N} \text{- Z-direction with rate } 3 \text{ N} \text{Therefore, momentum is changing in all three directions: X, Y, and Z.}

Import JSON File

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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
}