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Current Question (ID: 19027)

Question:

$\text{Train A and Train B are running on parallel tracks in opposite directions with speeds of } 36 \text{ km/h and } 72 \text{ km/h, respectively. A person is walking inside Train A in the direction opposite to the train's motion with a speed of } 1.8 \text{ km/h. What is the speed of this person as observed from Train B? (Assume the distance between the tracks is negligible.)}$

Options:

1. $30.5 \text{ m/s}$
2. $29.5 \text{ m/s}$
3. $31.5 \text{ m/s}$
4. $28.5 \text{ m/s}$

Solution:

$\text{Hint: Use the concept of relative velocity.}$ $\text{Step 1: Draw the diagram.}$ $\text{Step 2: Find the velocity of person with respect to ground.}$ $\text{The velocity of person relative to train A is given as:}$ $\vec{v}_{p/A} = -1.8$ $\Rightarrow \vec{v}_p - \vec{v}_A = -1.8$ $\Rightarrow \vec{v}_p - 36 = -1.8$ $\Rightarrow \vec{v}_p = 34.2 \text{ km/h}$ $\text{Step 3: Find the speed of the person as observed from train B.}$ $\vec{v}_{p/B} = \vec{v}_p - \vec{v}_B$ $\Rightarrow \vec{v}_{p/B} = 34.2 - (-72)$ $\Rightarrow \vec{v}_{p/B} = 106.2 \text{ km/h}$ $\Rightarrow \vec{v}_{p/B} = 106.2 \times \frac{5}{18} \text{ m/s}$ $\Rightarrow \vec{v}_{p/B} = 29.5 \text{ m/s}$ $\text{Hence, option (2) is the correct answer.}$

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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
}