Import Question JSON

Current Question (ID: 8919)

Question:

$\text{Two balls are projected upward simultaneously with speeds of } 40 \text{ m/s and } 60 \text{ m/s. The relative position } (x) \text{ of the second ball with respect to the first ball at time } t = 5 \text{ s will be: (neglect air resistance)}$

Options:

1. $20 \text{ m}$
2. $80 \text{ m}$
3. $100 \text{ m}$
4. $120 \text{ m}$

Solution:

$\text{Hint: } s = ut + \frac{1}{2}at^2$ $\text{Step: Find the relative position of the second ball with respect to the first ball at time } t = 5 \text{ sec.}$ $\text{Speed of the first ball } = 40 \text{ m/s}$ $\text{Speed of the second ball } = 60 \text{ m/s}$ $\text{Time, } t = 5 \text{ sec}$ $\text{Distance covered by the first ball:}$ $s_1 = 40 \times 5 - \frac{1}{2} \times 10 \times (5)^2 = 200 - 125 = 75 \text{ m}$ $\text{Distance covered by the second ball:}$ $s_2 = 60 \times 5 - \frac{1}{2} \times 10 \times (5)^2 = 300 - 125 = 175 \text{ m}$ $\text{Therefore, the relative position of the second ball w.r.t. the first ball } = 175 - 75 = 100 \text{ m}$ $\text{Hence, option (3) is the correct answer.}$

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
}