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Current Question (ID: 15955)

Question:

$y-x$ \text{ graph of a travelling wave along } +x \text{ direction is shown at any instant } t. \text{ (Symbols have their usual meanings). The velocity of a particle at:}$

Options:

1. $x_1 \text{ is downward}$
2. $x_2 \text{ is downward}$
3. $x_3 \text{ is upward}$
4. $x_4 \text{ is downward}$

Solution:

$\text{Hint: } v_p = -v \cdot \frac{dy}{dx}$ $\text{Step: Find the direction of the velocity of different particles.}$ $v_p = -v \cdot \frac{dy}{dx}$ $(1) \text{ At } x_1, \text{ slope is negative so particle velocity will be positive (upward).}$ $(2) \text{ At } x_2, \text{ the slope is positive so particle velocity will be negative (downward).}$ $(3) \text{ At } x_3, \text{ the particle is at an extreme position therefore the velocity will be downward.}$ $(4) \text{ At } x_4, \text{ the particle velocity will be upward as it moves towards the right.}$

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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
}