Import Question JSON

Current Question (ID: 9682)

Question:

$\text{Two particles are separated by a horizontal distance } x \text{ as shown in the figure. They are projected at the same time as shown in the figure with different initial speeds. The time after which the horizontal distance between them becomes zero will be:}$

Options:

1. $\frac{x}{u}$
2. $\frac{u}{2x}$
3. $\frac{2u}{x}$
4. $\text{None of the above}$

Solution:

\text{Hint: Time taken} = \frac{\text{distance}}{\text{velocity}} \text{Step: Find the time after which the horizontal distance becomes zero.} \text{Let } x_1 \text{ and } x_2 \text{ be the horizontal distances traveled by particles A and B, respectively, in time } t. x_1 = \frac{u}{\sqrt{3}} \cdot \cos(30°) \times t \quad \text{...(1)} \text{and } x_2 = u \cos(60°) \times t \quad \text{...(2)} \text{Since both particles move towards each other, their relative separation becomes zero when:} x_1 + x_2 = x \frac{u}{\sqrt{3}} \cdot \cos(30°) \times t + u \cos(60°) \times t = x t \left[\frac{u}{\sqrt{3}} \cdot \frac{\sqrt{3}}{2} + u \cdot \frac{1}{2}\right] = x t \left[\frac{u}{2} + \frac{u}{2}\right] = x t \cdot u = x \text{Therefore: } t = \frac{x}{u} \text{Hence, option (1) is the correct answer.}

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
}