Import Question JSON

Current Question (ID: 9591)

Question:

$\text{River of width 500 m is flowing at a speed of 10 m/s. A swimmer can swim at a speed of 10 m/s in still water. If he starts swimming at an angle of 120° with the flow direction, then the distance he travels along the river while crossing the river is:}$

Options:

1. $\text{250 m}$
2. $500\sqrt{3}\text{ m}$
3. $\frac{500}{\sqrt{3}}\text{ m}$
4. $\text{500 m}$

Solution:

$\text{Hint: Resolve } \vec{v}_{M,R}$ $\text{Step 1: Draw the diagram}$ $\text{The swimmer makes an angle of 120° with the flow direction. This means the angle with the perpendicular to the river bank is 30°.}$ $v_x = 10 - 10 \sin 30° = 5 \text{ m/s}$ $v_y = 10 \cos 30° = 5\sqrt{3} \text{ m/s}$ $\text{Step 2: Find the time taken to cross the river}$ $t = \frac{d}{v_y} = \frac{500}{5\sqrt{3}} = \frac{100}{\sqrt{3}} \text{ s}$ $\text{Step 3: Calculate the horizontal drift for man}$ $x = v_x t$ $= 5 \times \frac{100}{\sqrt{3}}$ $= \frac{500}{\sqrt{3}} \text{ m}$

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
}