Import Question JSON

Current Question (ID: 8923)

Question:

$\text{A bus is moving with a speed of 10 ms}^{-1} \text{ on a straight road. A scooterist wishes to overtake the bus in 100 s. If the bus is at a distance of 1 km from the scooterist, with what minimum speed should the scooterist chase the bus?}$

Options:

1. $20 \text{ ms}^{-1}$
2. $40 \text{ ms}^{-1}$
3. $25 \text{ ms}^{-1}$
4. $10 \text{ ms}^{-1}$

Solution:

$\text{Hint: Use the concept of relative velocity.}$ $\text{Step: Find the minimum speed of the scooterist.}$ $\text{Let } v \text{ be the relative velocity of scooter(s) w.r.t bus (B), then}$ $v = v_S - v_B$ $\text{Since both are moving in the same direction:}$ $v_S = v + v_B \quad \ldots(i)$ $\text{Relative velocity} = \frac{\text{displacement}}{\text{time}}$ $= \frac{1000}{100} = 10 \text{ ms}^{-1}$ $\text{Now, substituting the value of } v \text{ in Eq. (i), we get}$ $v_S = 10 + 10 = 20 \text{ ms}^{-1}$ $\text{Hence, option (1) is the correct answer.}$

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
}