Import Question JSON

Current Question (ID: 9683)

Question:

$\text{Balls A and B are thrown from two points lying on the same horizontal plane separated by a distance of 120 m. Which of the following statements is correct?}$

Options:

1. $\text{The balls can never meet.}$
2. $\text{The balls can meet if the ball B is thrown 1 s later.}$
3. $\text{The two balls meet at a height of 45 m.}$
4. $\text{None of the above}$

Solution:

$\text{Hint: To meet, the relative velocity should be zero in vertical direction}$ $\text{Step 1: Resolve velocity of ball A}$ $\vec{V}_A = 40\hat{i} + 30\hat{j}$ $\vec{V}_B = 30\hat{j}$ $\text{Step 2: Analyze motion of ball A in frame of ball B}$ $\vec{V}_{A,B} = \vec{V}_A - \vec{V}_B = 40\hat{i}$ $\vec{a}_{A,B} = -g + g = 0 \text{ m/s}^2$ $\text{Step 3: Find time of meeting of ball}$ $\text{Since ball A moves with constant velocity 40 m/s horizontally relative to ball B:}$ $t = \frac{120}{40} = 3\text{s}$ $\text{Step 4: Find vertical height at time of meeting}$ $y_B = u_B t - \frac{1}{2}gt^2$ $= 30 \times 3 - \frac{1}{2} \times 10 \times 3^2$ $= 45 \text{ m}$

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
}